{"id":333,"date":"2018-04-17T00:04:50","date_gmt":"2018-04-17T00:04:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=333"},"modified":"2024-04-26T22:03:36","modified_gmt":"2024-04-26T22:03:36","slug":"expressions-with-percents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/chapter\/expressions-with-percents\/","title":{"raw":"Solving Problems Using Percents","rendered":"Solving Problems Using Percents"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcome<\/h3>\r\n<ul>\r\n \t<li>Evaluate expressions and word problems involving percents<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p data-type=\"title\">In this section we will solve percent questions by identifying the parts of the problem. We'll look at a common application of percent\u2014tips to a server at a restaurant\u2014to see how to set up a basic percent application.<\/p>\r\nWhen Aolani and her friends ate dinner at a restaurant, the bill came to [latex]\\text{\\$80}[\/latex]. They wanted to leave a [latex]20\\%[\/latex] tip. What amount would the tip be?\r\n\r\nTo solve this, we want to find what <em data-effect=\"italics\">amount<\/em> is [latex]20\\%[\/latex] of [latex]\\$80[\/latex]. The [latex]\\$80[\/latex] is called the <em data-effect=\"italics\">base<\/em>. The <em>percent<\/em> is the given [latex]20\\%[\/latex]. The amount of the tip would be [latex]0.20(80)[\/latex], or [latex]\\$16[\/latex] \u2014 see the image below. To find the amount of the tip, we multiplied the percent by the base.\r\n<p style=\"text-align: center;\">A [latex]20\\%[\/latex] tip for an [latex]\\$80[\/latex] restaurant bill comes out to [latex]\\$16[\/latex].<\/p>\r\n\r\n<h2><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221909\/CNX_BMath_Figure_06_02_001.png\" alt=\"The figure shows a customer copy of a restaurant receipt with the amount of the bill, $80, and the amount of the tip, $16. There is a group of bills totaling $16.\" data-media-type=\"image\/png\" \/><\/h2>\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3>Pieces of a Percent Problem<\/h3>\r\n<p style=\"padding-left: 30px;\">Percent problems involve three quantities:\u00a0 the <em><strong>base<\/strong><\/em> amount (the whole), the <em><strong>percent<\/strong><\/em>, and the <em><strong>amount<\/strong><\/em> (a part of the whole or partial amount).<\/p>\r\n<p style=\"padding-left: 30px;\">The amount is a percent of the base.<\/p>\r\n\r\n<\/div>\r\nLet's look at another example:\r\n\r\nJeff has a Guitar Strings coupon for [latex]15\\%[\/latex] off any purchase of [latex]$100[\/latex] or more. He wants to buy a used guitar that has a price tag of [latex]$220[\/latex] on it. Jeff wonders how much money the coupon will take off the original [latex]$220[\/latex] price. Problems involving percents will have some combination of these three quantities to work with: the <em>percent<\/em>, the <em>amount<\/em>, and the <em>base<\/em>. The percent has the percent symbol (%) or the word percent. In the problem above, [latex]15\\%[\/latex] is the percent off the purchase price. The base is the whole amount or original amount. In the problem above, the \"whole\" price of the guitar is [latex]$220[\/latex], which is the base. The amount is the unknown and what we will need to calculate.\r\n\r\nThere are thee cases: a missing amount, a missing percent or a missing base. Let's take a look at each possibility.\r\n<h2>Solving for the Amount<\/h2>\r\nWhen solving for the amount in a percent problem, you will multiply the percent (as a decimal or fraction) by the base. Typically we choose the decimal value for percent.\r\n<p style=\"text-align: center;\">[latex]\\text{percent}\\cdot{\\text{base}}=\\text{amount}[\/latex]<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind [latex]50\\%[\/latex] of [latex]20[\/latex]\r\n\r\nSolution:\r\n\r\nFirst identify each piece of the problem:\r\n<p style=\"padding-left: 30px;\">percent: [latex]50\\%[\/latex] or [latex].5[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">base: [latex]20[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">amount: unknown<\/p>\r\nNow plug them into your equation\u00a0[latex]\\text{percent}\\cdot{\\text{base}}=\\text{amount}[\/latex]\r\n<p style=\"text-align: center;\">[latex].5\\cdot{20}= ?[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex].5\\cdot{20}= 10[\/latex]<\/p>\r\n<p style=\"text-align: center;\">Therefore, [latex]10[\/latex] is the amount or part that is\u00a0[latex]50\\%[\/latex] of [latex]20[\/latex].<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWhat is [latex]25\\%[\/latex] of [latex]80[\/latex]?\r\n\r\n[reveal-answer q=\"813233\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"813233\"]\r\n\r\nThe base is [latex]80[\/latex] and the percent is [latex]25\\%[\/latex], so amount [latex]= 80(0.25) = 20[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]80094[\/ohm_question]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/jTM7ZMvAzsc\r\n<h2>Solving for the Percent<\/h2>\r\n<p style=\"text-align: left;\">When solving for the percent in a percent problem, you will divide the amount by the base. The equation above is rearranged and the percent will come back as a decimal of fraction you can report in the form asked of you.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\Large{\\frac{\\text{amount}}{\\text{base}}}\\normalsize=\\text{percent}[\/latex]<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWhat percent of [latex]320[\/latex] is [latex]80[\/latex]?\r\n\r\nSolution:\r\n\r\nFirst identify each piece of the problem:\r\n<p style=\"padding-left: 30px;\">percent:\u00a0unknown<\/p>\r\n<p style=\"padding-left: 30px;\">base: [latex]320[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">amount:\u00a0[latex]80[\/latex]<\/p>\r\nNow plug the values into your equation\u00a0[latex]\\Large{\\frac{\\text{amount}}{\\text{base}}}\\normalsize=\\text{percent}[\/latex]\r\n<p style=\"text-align: center;\">[latex]\\large\\frac{80}{320}\\normalsize=?[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\large\\frac{80}{320}\\normalsize=.25[\/latex]<\/p>\r\n<p style=\"text-align: center;\">Therefore, [latex]80[\/latex] is [latex]25\\%[\/latex] of [latex]320[\/latex].<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\n[ohm_question]80097[\/ohm_question]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/p2KHHFMhJRs\r\n<h2>Solving for the Base<\/h2>\r\n<p style=\"text-align: left;\">When solving for the base in a percent problem, you will divide the amount by the percent (as a decimal or fraction). The equation above is rearranged and you will find the base after plugging in the values.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\Large{\\frac{\\text{amount}}{\\text{percent}}}\\normalsize=\\text{base}[\/latex]<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>EXample<\/h3>\r\n[latex]60[\/latex] is [latex]40\\%[\/latex] of what number?\r\n\r\nSolution:\r\n\r\nFirst identify each piece of the problem:\r\n<p style=\"padding-left: 30px;\">percent:[latex]40\\%[\/latex] or\u00a0[latex].4[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">base: unknown<\/p>\r\n<p style=\"padding-left: 30px;\">amount:\u00a0[latex]60[\/latex]<\/p>\r\nNow plug the values into your equation\u00a0[latex]\\Large{\\frac{\\text{amount}}{\\text{percent}}}\\normalsize=\\text{base}[\/latex]\r\n<p style=\"text-align: center;\">[latex](60)\\div(.4)=?[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex](60)\\div(.4)=150[\/latex]<\/p>\r\n<p style=\"text-align: center;\">Therefore, [latex]60[\/latex] is [latex]40\\%[\/latex] of [latex]150[\/latex].<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAn article says that [latex]15\\%[\/latex] of a non-profit\u2019s donations, about [latex]$30,000[\/latex] a year, comes from individual donors.\u00a0 What is the total amount of donations the non-profit receives?\r\n\r\n[reveal-answer q=\"731314\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"731314\"]\r\n\r\nThe percent is [latex]15\\%[\/latex], and [latex]$30,000[\/latex] is the amount (or part of the whole). We are looking for the base.\r\n\r\n<em>base<\/em>\u00a0= [latex]30000\\div(.15)=$200000[\/latex]\r\n\r\nThe non-profit receives [latex]$200000[\/latex] a year in donations\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\n[ohm_question]157022[\/ohm_question]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/3etjmUw8K3A\r\n<p data-type=\"title\">Here are a few more percent problems for you to try.<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146672[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146692[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146693[\/ohm_question]\r\n\r\n<\/div>\r\n<p data-type=\"title\">Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we'll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was [latex]\\text{\\$68.50}[\/latex]. They want to leave an [latex]\\text{18%}[\/latex] tip. If the tip will be [latex]\\text{18%}[\/latex] of the total bill, how much should the tip be?\r\n\r\nSolution\r\n<table id=\"eip-id1168468710061\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '144 is what percent of 96?' The first step is to translate the words into algebra, writing 144 as 144, representing the word 'is' with an equals sign, letting the variable p be equal to the percent, representing the word 'of' with a multiplication dot, and writing 96 as 96. The result is the equation 144 = p \u00b7 96. The second step is to divide both sides of the equation by 96. The third step is to simplify. The result is 1.5 = p. The fourth step is to convert the decimal to a percent. 150% = p. 144 is 150% of 96.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>What are you asked to find?<\/td>\r\n<td>the amount of the tip<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What formula\/equation should you use?<\/td>\r\n<td>[latex]\\text{percent}\\cdot{\\text{base}}=\\text{amount}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute in the correct values.<\/td>\r\n<td>[latex](.18)\\cdot{68.50}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Solve.<\/td>\r\n<td>\u00a0[latex](.18)\\cdot{68.50}=12.33[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The couple should leave a tip of [latex]\\text{\\$12.33}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146694[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we show another example of finding how much tip to give based on percent.\r\n\r\nhttps:\/\/youtu.be\/yFaa2CMx9rk\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe label on Masao's breakfast cereal said that one serving of cereal provides [latex]85[\/latex] milligrams (mg) of potassium, which is [latex]\\text{2%}[\/latex] of the recommended daily amount. What is the total recommended daily amount of potassium?\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221942\/CNX_BMath_Figure_06_02_002.png\" alt=\"The figures shows the nutrition facts for cereal.\" data-media-type=\"image\/png\" \/>\r\n[reveal-answer q=\"744443\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"744443\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468583805\" class=\"unnumbered unstyled\" style=\"width: 751px; height: 150px;\" summary=\"The figure shows the steps to solve the percent problem. Determine what you are asked to find. That is the total amount of potassium recommended. Choose a variable to represent the total amount of potassium. Let the variable a be equal to the total amount of potassium. Write a sentence that gives the information to find the total amount of the potassium. That sentence is '85 milligrams is 2% of the total amount.' Translate the sentence into an equation, writing 85 milligrams as 85, representing the word 'is' with an equals sign, writing 2% as 0.02, representing the word 'of' with a multiplication dot, and writing a as a. The result is the equation 85 = 0.02 \u00b7 a. Divide both sides of the equation by 0.02. Simplify. The result is the equation 4,250 = a. Write a complete sentence that answers the question. The sentence is 'The amount of potassium that is recommended is 4,250 milligrams. Check the reasonableness of the answer. It is reasonable because 2% is a small percent and 85 is a small part of 4,250.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 321px; height: 15px;\">What are you asked to find?<\/td>\r\n<td style=\"width: 430px; height: 15px;\">the total daily amount of potassium recommended (whole)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 321px; height: 15px;\">What formula\/equation should you use?<\/td>\r\n<td style=\"width: 430px; height: 15px;\">[latex]\\Large{\\frac{\\text{amount}}{\\text{percent}}}\\normalsize=\\text{base}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 321px; height: 15px;\">Substitute in the correct values.<\/td>\r\n<td style=\"width: 430px; height: 15px;\">[latex]\\Large{\\frac{85}{.02}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 321px; height: 15px;\">Solve.<\/td>\r\n<td style=\"width: 430px; height: 15px;\">[latex]\\Large{\\frac{85}{.02}}\\normalsize=4250[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px;\">\r\n<td style=\"width: 321px; height: 30px;\">Write a complete sentence that answers the question.<\/td>\r\n<td style=\"width: 430px; height: 30px;\">The amount of potassium that is recommended is [latex]4,250[\/latex] mg.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146697[\/ohm_question]\r\n\r\n[ohm_question]146702[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146703[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcome<\/h3>\n<ul>\n<li>Evaluate expressions and word problems involving percents<\/li>\n<\/ul>\n<\/div>\n<p data-type=\"title\">In this section we will solve percent questions by identifying the parts of the problem. We&#8217;ll look at a common application of percent\u2014tips to a server at a restaurant\u2014to see how to set up a basic percent application.<\/p>\n<p>When Aolani and her friends ate dinner at a restaurant, the bill came to [latex]\\text{\\$80}[\/latex]. They wanted to leave a [latex]20\\%[\/latex] tip. What amount would the tip be?<\/p>\n<p>To solve this, we want to find what <em data-effect=\"italics\">amount<\/em> is [latex]20\\%[\/latex] of [latex]\\$80[\/latex]. The [latex]\\$80[\/latex] is called the <em data-effect=\"italics\">base<\/em>. The <em>percent<\/em> is the given [latex]20\\%[\/latex]. The amount of the tip would be [latex]0.20(80)[\/latex], or [latex]\\$16[\/latex] \u2014 see the image below. To find the amount of the tip, we multiplied the percent by the base.<\/p>\n<p style=\"text-align: center;\">A [latex]20\\%[\/latex] tip for an [latex]\\$80[\/latex] restaurant bill comes out to [latex]\\$16[\/latex].<\/p>\n<h2><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221909\/CNX_BMath_Figure_06_02_001.png\" alt=\"The figure shows a customer copy of a restaurant receipt with the amount of the bill, $80, and the amount of the tip, $16. There is a group of bills totaling $16.\" data-media-type=\"image\/png\" \/><\/h2>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3>Pieces of a Percent Problem<\/h3>\n<p style=\"padding-left: 30px;\">Percent problems involve three quantities:\u00a0 the <em><strong>base<\/strong><\/em> amount (the whole), the <em><strong>percent<\/strong><\/em>, and the <em><strong>amount<\/strong><\/em> (a part of the whole or partial amount).<\/p>\n<p style=\"padding-left: 30px;\">The amount is a percent of the base.<\/p>\n<\/div>\n<p>Let&#8217;s look at another example:<\/p>\n<p>Jeff has a Guitar Strings coupon for [latex]15\\%[\/latex] off any purchase of [latex]$100[\/latex] or more. He wants to buy a used guitar that has a price tag of [latex]$220[\/latex] on it. Jeff wonders how much money the coupon will take off the original [latex]$220[\/latex] price. Problems involving percents will have some combination of these three quantities to work with: the <em>percent<\/em>, the <em>amount<\/em>, and the <em>base<\/em>. The percent has the percent symbol (%) or the word percent. In the problem above, [latex]15\\%[\/latex] is the percent off the purchase price. The base is the whole amount or original amount. In the problem above, the &#8220;whole&#8221; price of the guitar is [latex]$220[\/latex], which is the base. The amount is the unknown and what we will need to calculate.<\/p>\n<p>There are thee cases: a missing amount, a missing percent or a missing base. Let&#8217;s take a look at each possibility.<\/p>\n<h2>Solving for the Amount<\/h2>\n<p>When solving for the amount in a percent problem, you will multiply the percent (as a decimal or fraction) by the base. Typically we choose the decimal value for percent.<\/p>\n<p style=\"text-align: center;\">[latex]\\text{percent}\\cdot{\\text{base}}=\\text{amount}[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find [latex]50\\%[\/latex] of [latex]20[\/latex]<\/p>\n<p>Solution:<\/p>\n<p>First identify each piece of the problem:<\/p>\n<p style=\"padding-left: 30px;\">percent: [latex]50\\%[\/latex] or [latex].5[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">base: [latex]20[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">amount: unknown<\/p>\n<p>Now plug them into your equation\u00a0[latex]\\text{percent}\\cdot{\\text{base}}=\\text{amount}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex].5\\cdot{20}= ?[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex].5\\cdot{20}= 10[\/latex]<\/p>\n<p style=\"text-align: center;\">Therefore, [latex]10[\/latex] is the amount or part that is\u00a0[latex]50\\%[\/latex] of [latex]20[\/latex].<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>What is [latex]25\\%[\/latex] of [latex]80[\/latex]?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q813233\">Show Answer<\/span><\/p>\n<div id=\"q813233\" class=\"hidden-answer\" style=\"display: none\">\n<p>The base is [latex]80[\/latex] and the percent is [latex]25\\%[\/latex], so amount [latex]= 80(0.25) = 20[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm80094\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=80094&theme=oea&iframe_resize_id=ohm80094&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Find the Percent of a Number\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/jTM7ZMvAzsc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Solving for the Percent<\/h2>\n<p style=\"text-align: left;\">When solving for the percent in a percent problem, you will divide the amount by the base. The equation above is rearranged and the percent will come back as a decimal of fraction you can report in the form asked of you.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large{\\frac{\\text{amount}}{\\text{base}}}\\normalsize=\\text{percent}[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>What percent of [latex]320[\/latex] is [latex]80[\/latex]?<\/p>\n<p>Solution:<\/p>\n<p>First identify each piece of the problem:<\/p>\n<p style=\"padding-left: 30px;\">percent:\u00a0unknown<\/p>\n<p style=\"padding-left: 30px;\">base: [latex]320[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">amount:\u00a0[latex]80[\/latex]<\/p>\n<p>Now plug the values into your equation\u00a0[latex]\\Large{\\frac{\\text{amount}}{\\text{base}}}\\normalsize=\\text{percent}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\large\\frac{80}{320}\\normalsize=?[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\large\\frac{80}{320}\\normalsize=.25[\/latex]<\/p>\n<p style=\"text-align: center;\">Therefore, [latex]80[\/latex] is [latex]25\\%[\/latex] of [latex]320[\/latex].<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm80097\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=80097&theme=oea&iframe_resize_id=ohm80097&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Use the Percent Equation to Find a Percent\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/p2KHHFMhJRs?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Solving for the Base<\/h2>\n<p style=\"text-align: left;\">When solving for the base in a percent problem, you will divide the amount by the percent (as a decimal or fraction). The equation above is rearranged and you will find the base after plugging in the values.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large{\\frac{\\text{amount}}{\\text{percent}}}\\normalsize=\\text{base}[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>EXample<\/h3>\n<p>[latex]60[\/latex] is [latex]40\\%[\/latex] of what number?<\/p>\n<p>Solution:<\/p>\n<p>First identify each piece of the problem:<\/p>\n<p style=\"padding-left: 30px;\">percent:[latex]40\\%[\/latex] or\u00a0[latex].4[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">base: unknown<\/p>\n<p style=\"padding-left: 30px;\">amount:\u00a0[latex]60[\/latex]<\/p>\n<p>Now plug the values into your equation\u00a0[latex]\\Large{\\frac{\\text{amount}}{\\text{percent}}}\\normalsize=\\text{base}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex](60)\\div(.4)=?[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex](60)\\div(.4)=150[\/latex]<\/p>\n<p style=\"text-align: center;\">Therefore, [latex]60[\/latex] is [latex]40\\%[\/latex] of [latex]150[\/latex].<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>An article says that [latex]15\\%[\/latex] of a non-profit\u2019s donations, about [latex]$30,000[\/latex] a year, comes from individual donors.\u00a0 What is the total amount of donations the non-profit receives?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q731314\">Show Answer<\/span><\/p>\n<div id=\"q731314\" class=\"hidden-answer\" style=\"display: none\">\n<p>The percent is [latex]15\\%[\/latex], and [latex]$30,000[\/latex] is the amount (or part of the whole). We are looking for the base.<\/p>\n<p><em>base<\/em>\u00a0= [latex]30000\\div(.15)=$200000[\/latex]<\/p>\n<p>The non-profit receives [latex]$200000[\/latex] a year in donations<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm157022\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=157022&theme=oea&iframe_resize_id=ohm157022&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Use a Percent Equation to Solve for a Base or Whole Amount\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/3etjmUw8K3A?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p data-type=\"title\">Here are a few more percent problems for you to try.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146672\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146672&theme=oea&iframe_resize_id=ohm146672&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146692\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146692&theme=oea&iframe_resize_id=ohm146692&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146693\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146693&theme=oea&iframe_resize_id=ohm146693&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p data-type=\"title\">Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we&#8217;ll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Dezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was [latex]\\text{\\$68.50}[\/latex]. They want to leave an [latex]\\text{18%}[\/latex] tip. If the tip will be [latex]\\text{18%}[\/latex] of the total bill, how much should the tip be?<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468710061\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '144 is what percent of 96?' The first step is to translate the words into algebra, writing 144 as 144, representing the word 'is' with an equals sign, letting the variable p be equal to the percent, representing the word 'of' with a multiplication dot, and writing 96 as 96. The result is the equation 144 = p \u00b7 96. The second step is to divide both sides of the equation by 96. The third step is to simplify. The result is 1.5 = p. The fourth step is to convert the decimal to a percent. 150% = p. 144 is 150% of 96.\" data-label=\"\">\n<tbody>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>the amount of the tip<\/td>\n<\/tr>\n<tr>\n<td>What formula\/equation should you use?<\/td>\n<td>[latex]\\text{percent}\\cdot{\\text{base}}=\\text{amount}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute in the correct values.<\/td>\n<td>[latex](.18)\\cdot{68.50}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Solve.<\/td>\n<td>\u00a0[latex](.18)\\cdot{68.50}=12.33[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The couple should leave a tip of [latex]\\text{\\$12.33}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146694\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146694&theme=oea&iframe_resize_id=ohm146694&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we show another example of finding how much tip to give based on percent.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Percent Application - Tipping\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/yFaa2CMx9rk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The label on Masao&#8217;s breakfast cereal said that one serving of cereal provides [latex]85[\/latex] milligrams (mg) of potassium, which is [latex]\\text{2%}[\/latex] of the recommended daily amount. What is the total recommended daily amount of potassium?<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221942\/CNX_BMath_Figure_06_02_002.png\" alt=\"The figures shows the nutrition facts for cereal.\" data-media-type=\"image\/png\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q744443\">Show Answer<\/span><\/p>\n<div id=\"q744443\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468583805\" class=\"unnumbered unstyled\" style=\"width: 751px; height: 150px;\" summary=\"The figure shows the steps to solve the percent problem. Determine what you are asked to find. That is the total amount of potassium recommended. Choose a variable to represent the total amount of potassium. Let the variable a be equal to the total amount of potassium. Write a sentence that gives the information to find the total amount of the potassium. That sentence is '85 milligrams is 2% of the total amount.' Translate the sentence into an equation, writing 85 milligrams as 85, representing the word 'is' with an equals sign, writing 2% as 0.02, representing the word 'of' with a multiplication dot, and writing a as a. The result is the equation 85 = 0.02 \u00b7 a. Divide both sides of the equation by 0.02. Simplify. The result is the equation 4,250 = a. Write a complete sentence that answers the question. The sentence is 'The amount of potassium that is recommended is 4,250 milligrams. Check the reasonableness of the answer. It is reasonable because 2% is a small percent and 85 is a small part of 4,250.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 321px; height: 15px;\">What are you asked to find?<\/td>\n<td style=\"width: 430px; height: 15px;\">the total daily amount of potassium recommended (whole)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 321px; height: 15px;\">What formula\/equation should you use?<\/td>\n<td style=\"width: 430px; height: 15px;\">[latex]\\Large{\\frac{\\text{amount}}{\\text{percent}}}\\normalsize=\\text{base}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 321px; height: 15px;\">Substitute in the correct values.<\/td>\n<td style=\"width: 430px; height: 15px;\">[latex]\\Large{\\frac{85}{.02}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 321px; height: 15px;\">Solve.<\/td>\n<td style=\"width: 430px; height: 15px;\">[latex]\\Large{\\frac{85}{.02}}\\normalsize=4250[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 321px; height: 30px;\">Write a complete sentence that answers the question.<\/td>\n<td style=\"width: 430px; height: 30px;\">The amount of potassium that is recommended is [latex]4,250[\/latex] mg.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146697\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146697&theme=oea&iframe_resize_id=ohm146697&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146702\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146702&theme=oea&iframe_resize_id=ohm146702&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146703\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146703&theme=oea&iframe_resize_id=ohm146703&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-333\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Revision and Adaptation of DevMath. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/arithmetic\/arith3-5.pdf\">http:\/\/www.opentextbookstore.com\/arithmetic\/arith3-5.pdf<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":18,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Revision and Adaptation of DevMath\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\"http:\/\/www.opentextbookstore.com\/arithmetic\/arith3-5.pdf\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"3dd72215-9cf1-4352-9c17-479ab430838e, 6e525a8d-6994-4ea7-bf87-c2ee5821ea00","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-333","chapter","type-chapter","status-publish","hentry"],"part":22,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/333","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":33,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/333\/revisions"}],"predecessor-version":[{"id":3247,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/333\/revisions\/3247"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/parts\/22"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/333\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/media?parent=333"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapter-type?post=333"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/contributor?post=333"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/license?post=333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}