{"id":4474,"date":"2020-04-13T14:21:10","date_gmt":"2020-04-13T14:21:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4474"},"modified":"2020-04-13T14:21:10","modified_gmt":"2020-04-13T14:21:10","slug":"finding-percent-increase-and-percent-decrease","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/finding-percent-increase-and-percent-decrease\/","title":{"raw":"Finding Percent Increase and Percent Decrease","rendered":"Finding Percent Increase and Percent Decrease"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find percent increase given two values<\/li>\r\n \t<li>Find percent decrease given two values<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.<\/p>\r\nTo find the percent increase, first we find the amount of increase, which is the difference between the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.\r\n<div class=\"textbox shaded\">\r\n<h3>Find Percent Increase<\/h3>\r\nStep 1. Find the amount of increase.\r\n<ul id=\"fs-id1166490916546\">\r\n \t<li>[latex]\\text{increase}=\\text{new amount}-\\text{original amount}[\/latex]<\/li>\r\n<\/ul>\r\nStep 2. Find the percent increase as a percent of the original amount.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nIn [latex]2011[\/latex], the California governor proposed raising community college fees from [latex]\\text{\\$26}[\/latex] per unit to [latex]\\text{\\$36}[\/latex] per unit. Find the percent increase. (Round to the nearest tenth of a percent.)\r\n\r\nSolution\r\n<table id=\"eip-id1168466580305\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solve the percent problem. Determine what you are asked to find. That is the percent increase. Choose a variable to represent the percent increase. Let the variable p be equal to percent increase. Find the amount of the increase. 36, the new amount, minus, 26, the original amount, is equal to 10, the amount of the increase. Find the percent increase. The increase is what percent of the original amount? Translate it into an equation, writing 10 as 10, representing the word 'is' with an equals sign, letting p be equal to the percent, representing the word 'of' with a multiplication dot, and writing 26 as 26. The result is the equation 10 is equal to p times 26. Divide both sides by 26. Round the nearest thousandth. The result is 0.384 is equal to p. Convert the decimal to percent form. 38.4% is equal to p. Write the answer as a complete sentence. The new fees represent a 38.4% increase over the old fees.\">\r\n<tbody>\r\n<tr>\r\n<td>What are you asked to find?<\/td>\r\n<td>the percent increase<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]p=[\/latex] percent.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the amount of increase.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221954\/CNX_BMath_Figure_06_02_012_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the percent increase.<\/td>\r\n<td>The increase is what percent of the original amount?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to an equation.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221956\/CNX_BMath_Figure_06_02_012_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by [latex]26[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{10}{26}}={\\Large\\frac{26p}{26}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Round to the nearest thousandth.<\/td>\r\n<td>[latex]0.385=p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to percent form.<\/td>\r\n<td>[latex]\\text{38.5%}=p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence.<\/td>\r\n<td>The new fees represent a [latex]38.5\\text{%}[\/latex] increase over the old fees.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146704[\/ohm_question]\r\n\r\n[ohm_question]146705[\/ohm_question]\r\n\r\n<\/div>\r\nFinding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference between the original amount and the final amount. Then we find what percent the amount of decrease is of the original amount.\r\n<div class=\"textbox shaded\">\r\n<h3>Find percent decrease<\/h3>\r\n<ol id=\"eip-id1168467275132\" class=\"stepwise\">\r\n \t<li>Find the amount of decrease.\r\n<ul id=\"eip-id1168467275136\">\r\n \t<li>[latex]\\text{decrease}=\\text{original amount}-\\text{new amount}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Find the percent decrease as a percent of the original amount.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe average price of a gallon of gas in one city in June [latex]2014[\/latex] was [latex]\\text{\\$3.71}[\/latex]. The average price in that city in July was [latex]\\text{\\$3.64}[\/latex]. Find the percent decrease.\r\n[reveal-answer q=\"516647\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"516647\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468530154\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solve the percent problem. Determine what you are asked to find. That is the percent decrease. Choose a variable to represent the percent decrease. Let the variable p be equal to percent decrease. Find the amount of the decrease. 3.71, the original amount, minus, 3.64, the new amount, is equal to 0.07, the amount of the decrease. Find the percent decrease. The decrease is what percent of the original amount? Translate it into an equation, writing 0.07 as 0.07, representing the word 'is' with an equals sign, letting p be equal to the percent, representing the word 'of' with a multiplication dot, and writing 3.71 as 3.71. The result is the equation 0.07 = p \u00b7 3.71. Divide both sides by 3.71. Round to the nearest thousandth. The result is 0.019 is equal to p. Convert the decimal to percent form. 1.9% = p. Write the answer as a complete sentence. The price of gas decreased 1.9%.\">\r\n<tbody>\r\n<tr>\r\n<td>What are you asked to find?<\/td>\r\n<td>the percent decrease<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]p=[\/latex] percent.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the amount of decrease.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222002\/CNX_BMath_Figure_06_02_013_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the percent of decrease.<\/td>\r\n<td>The decrease is what percent of the original amount?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to an equation.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222004\/CNX_BMath_Figure_06_02_013_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by [latex]3.71[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{0.07}{3.71}}={\\Large\\frac{3.71p}{3.71}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Round to the nearest thousandth.<\/td>\r\n<td>[latex]0.019=p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to percent form.<\/td>\r\n<td>[latex]\\text{1.9%}=p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence.<\/td>\r\n<td>The price of gas decreased [latex]1.9\\text{%}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146706[\/ohm_question]\r\n\r\n[ohm_question]146707[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to find percent increase and decrease.\r\n\r\nhttps:\/\/youtu.be\/mfe__iO5fbk","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find percent increase given two values<\/li>\n<li>Find percent decrease given two values<\/li>\n<\/ul>\n<\/div>\n<p>People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.<\/p>\n<p>To find the percent increase, first we find the amount of increase, which is the difference between the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.<\/p>\n<div class=\"textbox shaded\">\n<h3>Find Percent Increase<\/h3>\n<p>Step 1. Find the amount of increase.<\/p>\n<ul id=\"fs-id1166490916546\">\n<li>[latex]\\text{increase}=\\text{new amount}-\\text{original amount}[\/latex]<\/li>\n<\/ul>\n<p>Step 2. Find the percent increase as a percent of the original amount.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>In [latex]2011[\/latex], the California governor proposed raising community college fees from [latex]\\text{\\$26}[\/latex] per unit to [latex]\\text{\\$36}[\/latex] per unit. Find the percent increase. (Round to the nearest tenth of a percent.)<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168466580305\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solve the percent problem. Determine what you are asked to find. That is the percent increase. Choose a variable to represent the percent increase. Let the variable p be equal to percent increase. Find the amount of the increase. 36, the new amount, minus, 26, the original amount, is equal to 10, the amount of the increase. Find the percent increase. The increase is what percent of the original amount? Translate it into an equation, writing 10 as 10, representing the word 'is' with an equals sign, letting p be equal to the percent, representing the word 'of' with a multiplication dot, and writing 26 as 26. The result is the equation 10 is equal to p times 26. Divide both sides by 26. Round the nearest thousandth. The result is 0.384 is equal to p. Convert the decimal to percent form. 38.4% is equal to p. Write the answer as a complete sentence. The new fees represent a 38.4% increase over the old fees.\">\n<tbody>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>the percent increase<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]p=[\/latex] percent.<\/td>\n<\/tr>\n<tr>\n<td>Find the amount of increase.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221954\/CNX_BMath_Figure_06_02_012_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Find the percent increase.<\/td>\n<td>The increase is what percent of the original amount?<\/td>\n<\/tr>\n<tr>\n<td>Translate to an equation.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221956\/CNX_BMath_Figure_06_02_012_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by [latex]26[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{10}{26}}={\\Large\\frac{26p}{26}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Round to the nearest thousandth.<\/td>\n<td>[latex]0.385=p[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert to percent form.<\/td>\n<td>[latex]\\text{38.5%}=p[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>The new fees represent a [latex]38.5\\text{%}[\/latex] increase over the old fees.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146704\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146704&theme=oea&iframe_resize_id=ohm146704&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146705\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146705&theme=oea&iframe_resize_id=ohm146705&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Finding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference between the original amount and the final amount. Then we find what percent the amount of decrease is of the original amount.<\/p>\n<div class=\"textbox shaded\">\n<h3>Find percent decrease<\/h3>\n<ol id=\"eip-id1168467275132\" class=\"stepwise\">\n<li>Find the amount of decrease.\n<ul id=\"eip-id1168467275136\">\n<li>[latex]\\text{decrease}=\\text{original amount}-\\text{new amount}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>Find the percent decrease as a percent of the original amount.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The average price of a gallon of gas in one city in June [latex]2014[\/latex] was [latex]\\text{\\$3.71}[\/latex]. The average price in that city in July was [latex]\\text{\\$3.64}[\/latex]. Find the percent decrease.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q516647\">Show Solution<\/span><\/p>\n<div id=\"q516647\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468530154\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solve the percent problem. Determine what you are asked to find. That is the percent decrease. Choose a variable to represent the percent decrease. Let the variable p be equal to percent decrease. Find the amount of the decrease. 3.71, the original amount, minus, 3.64, the new amount, is equal to 0.07, the amount of the decrease. Find the percent decrease. The decrease is what percent of the original amount? Translate it into an equation, writing 0.07 as 0.07, representing the word 'is' with an equals sign, letting p be equal to the percent, representing the word 'of' with a multiplication dot, and writing 3.71 as 3.71. The result is the equation 0.07 = p \u00b7 3.71. Divide both sides by 3.71. Round to the nearest thousandth. The result is 0.019 is equal to p. Convert the decimal to percent form. 1.9% = p. Write the answer as a complete sentence. The price of gas decreased 1.9%.\">\n<tbody>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>the percent decrease<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]p=[\/latex] percent.<\/td>\n<\/tr>\n<tr>\n<td>Find the amount of decrease.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222002\/CNX_BMath_Figure_06_02_013_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Find the percent of decrease.<\/td>\n<td>The decrease is what percent of the original amount?<\/td>\n<\/tr>\n<tr>\n<td>Translate to an equation.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222004\/CNX_BMath_Figure_06_02_013_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by [latex]3.71[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{0.07}{3.71}}={\\Large\\frac{3.71p}{3.71}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Round to the nearest thousandth.<\/td>\n<td>[latex]0.019=p[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert to percent form.<\/td>\n<td>[latex]\\text{1.9%}=p[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>The price of gas decreased [latex]1.9\\text{%}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146706\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146706&theme=oea&iframe_resize_id=ohm146706&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146707\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146707&theme=oea&iframe_resize_id=ohm146707&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to find percent increase and decrease.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Determine Percent of Change - Increase and Decrease\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/mfe__iO5fbk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\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-4474\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146707, 146706, 146705, 146704, 146703. <strong>Authored by<\/strong>: Lumen Learning. <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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Determine Percent of Change - Increase and Decrease. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/mfe__iO5fbk\">https:\/\/youtu.be\/mfe__iO5fbk<\/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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":25777,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146707, 146706, 146705, 146704, 146703\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Determine Percent of Change - 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