{"id":4221,"date":"2020-04-08T02:29:33","date_gmt":"2020-04-08T02:29:33","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4221"},"modified":"2021-02-05T23:59:09","modified_gmt":"2021-02-05T23:59:09","slug":"solving-a-formula-for-a-specific-variable-2","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/solving-a-formula-for-a-specific-variable-2\/","title":{"raw":"Solving a Formula For a Specific Variable","rendered":"Solving a Formula For a Specific Variable"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Solve a formula for a specific variable using the properties of equality<\/li>\r\n \t<li>Evaluate a formula for given values of the variables<\/li>\r\n<\/ul>\r\n<\/div>\r\nFormulas are useful in the sciences and social sciences\u2014fields such as chemistry, physics, biology, psychology, sociology, and criminal justice. Healthcare workers use formulas, too, even for something as routine as dispensing medicine. The widely used spreadsheet program Microsoft Excel<sup>TM<\/sup> relies on formulas to do its calculations. Financial tools and calculators such as those in spreadsheets and applets offered by banks and financial advisors online also rely on formulas. Many teachers use spreadsheets to apply formulas to compute student grades. It is important to be familiar with formulas and be able to manipulate them easily.\r\n\r\nHere's an example that uses a formula you may have seen before:\u00a0 [latex]d=rt[\/latex], or <em>distance\u00a0<\/em>=\u00a0<em>rate <\/em>times\u00a0<em>time<\/em>. This formula gives the value of the distance [latex]d[\/latex] when you substitute in the values of a rate [latex]r[\/latex], and a time [latex]t[\/latex]. We encounter this formula every day in an alternate form: [latex]r=\\dfrac{d}{t}[\/latex], or the\u00a0<em>rate<\/em> =\u00a0<em>distance\u00a0<\/em>per\u00a0<em>time<\/em>. You may recognize it in the more familiar phrase describing a <em>rate<\/em> in\u00a0<em>miles\u00a0<\/em>per\u00a0<em>hour<\/em>. We are able to solve the original formula for the variable [latex]r[\/latex] by dividing [latex]t[\/latex] away on both sides. See the example below for a demonstration.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve the formula\u00a0 [latex]d=rt[\/latex] for [latex]r[\/latex].\r\n\r\nSolution:\r\n[latex]d=rt[\/latex]\r\n\r\n[latex]\\dfrac{d}{t}=\\dfrac{r \\cancel{t}}{\\cancel{t}}[\/latex]\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 divide by [latex]t[\/latex] on both sides\r\n\r\n[latex]\\dfrac{d}{t}=r[\/latex]\r\n\r\n<\/div>\r\nWe can also solve for [latex]t[\/latex]. And we can find the value of one of the variables by substituting in\u00a0particular values for the others. For example, to find the value of [latex]t[\/latex] for particular values of [latex]d[\/latex] and [latex]r[\/latex], we can first solve the formula for [latex]t[\/latex], then substitute in the particular values of [latex]d[\/latex] and [latex]r[\/latex]. Equations that are formulas for real-world relationships are often called\u00a0<em>literal<\/em><em> equations<\/em>, since the letters in the equation (the\u00a0<em>literals<\/em>) each stand for a real value. See more examples below of solving a formula for a specific variable.\r\n<div class=\"textbox shaded\"><strong>To solve a formula for a specific variable<\/strong> means to get that variable by itself with a coefficient of [latex]1[\/latex] on one side of the equation and all the other variables and constants on the other side. We will call this solving an equation for a specific variable <em>in general.<\/em> This process is also called <em>solving a literal equation<\/em>. The result is another formula, made up only of variables. The formula contains letters, or <em>literals<\/em>.<\/div>\r\nLet\u2019s try a few examples, starting with the distance, rate, and time formula we used above.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve the formula [latex]d=rt[\/latex] for [latex]t\\text{:}[\/latex]\r\n<ol>\r\n \t<li>When [latex]d=520[\/latex] and [latex]r=65[\/latex]<\/li>\r\n \t<li>In general.<\/li>\r\n<\/ol>\r\nSolution:\r\nWe\u2019ll write the solutions side-by-side so you can see that solving a formula in general uses the same steps as when we have numbers to substitute.\r\n<table id=\"eip-id1164150753614\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>1. When [latex]d = 520[\/latex] and [latex]r = 65[\/latex]<\/td>\r\n<td>2. In general<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the formula.<\/td>\r\n<td>[latex]d=rt[\/latex]<\/td>\r\n<td>[latex]d=rt[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute any given values.<\/td>\r\n<td>[latex]520=65t[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide to isolate <em>t<\/em>.<\/td>\r\n<td>[latex]{\\Large\\frac{520}{65}}={\\Large\\frac{65t}{65}}[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{d}{r}}={\\Large\\frac{rt}{r}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]8=t[\/latex][latex]t=8[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{d}{r}}=t[\/latex][latex]t={\\Large\\frac{d}{r}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nWe say the formula [latex]t={\\Large\\frac{d}{r}}[\/latex] is solved for [latex]t[\/latex]. We can use this version of the formula any time we are given the distance and rate and need to find the time.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145634&amp;theme=oea&amp;iframe_resize_id=mom225[\/embed]\r\n\r\n<\/div>\r\nThe formula [latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex] can be used to find the area of a triangle when given the base and height. In the next example, we will solve this formula for the height.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe formula for area of a triangle is [latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex]. Solve this formula for [latex]h\\text{:}[\/latex]\r\n<ol>\r\n \t<li>When [latex]A=90[\/latex] and [latex]b=15[\/latex]<\/li>\r\n \t<li>In general<\/li>\r\n<\/ol>\r\n<p class=\"p1\">[reveal-answer q=\"190834\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"190834\"]<\/p>\r\nSolution:\r\n<table id=\"eip-id1170572798895\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>1. When <em>A<\/em> = 90 and <em>b<\/em> = 15<\/td>\r\n<td>2. In general<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the forumla.<\/td>\r\n<td>[latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex]<\/td>\r\n<td>[latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute any given values.<\/td>\r\n<td>[latex]90=\\Large\\frac{1}{2}\\normalsize\\cdot{15}\\cdot{h}[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Clear the fractions.<\/td>\r\n<td>[latex]\\color{red}{2}\\cdot{90}=\\color{red}{2}\\cdot\\Large\\frac{1}{2}\\normalsize\\cdot{15}\\cdot{h}[\/latex]<\/td>\r\n<td>[latex]\\color{red}{2}\\cdot{A}=\\color{red}{2}\\cdot\\Large\\frac{1}{2}\\normalsize\\cdot{b}\\cdot{h}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]180=15h[\/latex]<\/td>\r\n<td>[latex]2A=bh[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Solve for <em>h<\/em>.<\/td>\r\n<td>[latex]12=h[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{2A}{b}}=h[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe can now find the height of a triangle, if we know the area and the base, by using the formula\r\n\r\n[latex]h={\\Large\\frac{2A}{b}}[\/latex]\r\n\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[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145635&amp;theme=oea&amp;iframe_resize_id=mom700[\/embed]\r\n\r\n<\/div>\r\nThe formula [latex]I=Prt[\/latex] is used to calculate simple interest, where [latex]I[\/latex] is interest, [latex]P[\/latex] is principal, [latex]r[\/latex] is rate as a decimal, and [latex]t[\/latex] is time in years.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve the formula [latex]I=Prt[\/latex] to find the principal, [latex]P\\text{:}[\/latex]\r\n<ol>\r\n \t<li>When [latex]I=\\text{\\$5,600},r=\\text{4%},t=7\\text{years}[\/latex]<\/li>\r\n \t<li>In general<\/li>\r\n<\/ol>\r\n<p class=\"p1\">[reveal-answer q=\"542986\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"542986\"]<\/p>\r\nSolution:\r\n<table id=\"eip-id1168058902092\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><em>1. \u00a0I<\/em> = $5600, <em>r<\/em> = 4%, <em>t<\/em> = 7 years<\/td>\r\n<td>2. In general<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the forumla.<\/td>\r\n<td>[latex]I=Prt[\/latex]<\/td>\r\n<td>[latex]I=Prt[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute any given values.<\/td>\r\n<td>[latex]5600=P(0.04)(7)[\/latex]<\/td>\r\n<td>[latex]I=Prt[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply <em>r<\/em> \u22c5 <em>t<\/em>.<\/td>\r\n<td>[latex]5600=P(0.28)[\/latex]<\/td>\r\n<td>[latex]I=P(rt)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide to isolate <em>P<\/em>.<\/td>\r\n<td>[latex]\\Large\\frac{5600}{\\color{red}{0.28}}\\normalsize =\\Large\\frac{P(0.28)}{\\color{red}{0.28}}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{I}{\\color{red}{rt}}\\normalsize =\\Large\\frac{P(rt)}{\\color{red}{rt}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]20,000=P[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{I}{rt}\\normalsize =P[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>State the answer.<\/td>\r\n<td>The principal is $20,000.<\/td>\r\n<td>[latex]P=\\Large\\frac{I}{rt}[\/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[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145640&amp;theme=oea&amp;iframe_resize_id=mom900[\/embed]\r\n\r\n<\/div>\r\nWatch the following video to see another\u00a0example of how to solve an equation for a specific variable.\r\n\r\nhttps:\/\/youtu.be\/VQZQvJ3rXYg\r\n\r\nThe following examples just ask you to solve a formula in general, without finding particular values.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve the formula [latex]P=a+b+c[\/latex] for [latex]a[\/latex].\r\n<p class=\"p1\">[reveal-answer q=\"872233\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"872233\"]<\/p>\r\nSolution:\r\nWe will isolate [latex]a[\/latex] on one side of the equation.\r\n<table id=\"eip-id1168469748609\" class=\"unnumbered unstyled\" summary=\"The top line says, \">\r\n<tbody>\r\n<tr>\r\n<td>We will isolate <em>a<\/em> on one side of the equation.<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the equation.<\/td>\r\n<td><\/td>\r\n<td>[latex]P=a+b+c[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract <em>b<\/em> and <em>c<\/em> from both sides to isolate <em>a<\/em>.<\/td>\r\n<td><\/td>\r\n<td>[latex]P\\color{red}{-b-c}=a+b+c\\color{red}{-b-c}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><\/td>\r\n<td>[latex]P-b-c=a[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSo, [latex]a=P-b-c[\/latex]\r\n\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&nbsp;\r\n\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142894&amp;theme=oea&amp;iframe_resize_id=mom20[\/embed]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Solve a formula for a specific variable using the properties of equality<\/li>\n<li>Evaluate a formula for given values of the variables<\/li>\n<\/ul>\n<\/div>\n<p>Formulas are useful in the sciences and social sciences\u2014fields such as chemistry, physics, biology, psychology, sociology, and criminal justice. Healthcare workers use formulas, too, even for something as routine as dispensing medicine. The widely used spreadsheet program Microsoft Excel<sup>TM<\/sup> relies on formulas to do its calculations. Financial tools and calculators such as those in spreadsheets and applets offered by banks and financial advisors online also rely on formulas. Many teachers use spreadsheets to apply formulas to compute student grades. It is important to be familiar with formulas and be able to manipulate them easily.<\/p>\n<p>Here&#8217;s an example that uses a formula you may have seen before:\u00a0 [latex]d=rt[\/latex], or <em>distance\u00a0<\/em>=\u00a0<em>rate <\/em>times\u00a0<em>time<\/em>. This formula gives the value of the distance [latex]d[\/latex] when you substitute in the values of a rate [latex]r[\/latex], and a time [latex]t[\/latex]. We encounter this formula every day in an alternate form: [latex]r=\\dfrac{d}{t}[\/latex], or the\u00a0<em>rate<\/em> =\u00a0<em>distance\u00a0<\/em>per\u00a0<em>time<\/em>. You may recognize it in the more familiar phrase describing a <em>rate<\/em> in\u00a0<em>miles\u00a0<\/em>per\u00a0<em>hour<\/em>. We are able to solve the original formula for the variable [latex]r[\/latex] by dividing [latex]t[\/latex] away on both sides. See the example below for a demonstration.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve the formula\u00a0 [latex]d=rt[\/latex] for [latex]r[\/latex].<\/p>\n<p>Solution:<br \/>\n[latex]d=rt[\/latex]<\/p>\n<p>[latex]\\dfrac{d}{t}=\\dfrac{r \\cancel{t}}{\\cancel{t}}[\/latex]\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 divide by [latex]t[\/latex] on both sides<\/p>\n<p>[latex]\\dfrac{d}{t}=r[\/latex]<\/p>\n<\/div>\n<p>We can also solve for [latex]t[\/latex]. And we can find the value of one of the variables by substituting in\u00a0particular values for the others. For example, to find the value of [latex]t[\/latex] for particular values of [latex]d[\/latex] and [latex]r[\/latex], we can first solve the formula for [latex]t[\/latex], then substitute in the particular values of [latex]d[\/latex] and [latex]r[\/latex]. Equations that are formulas for real-world relationships are often called\u00a0<em>literal<\/em><em> equations<\/em>, since the letters in the equation (the\u00a0<em>literals<\/em>) each stand for a real value. See more examples below of solving a formula for a specific variable.<\/p>\n<div class=\"textbox shaded\"><strong>To solve a formula for a specific variable<\/strong> means to get that variable by itself with a coefficient of [latex]1[\/latex] on one side of the equation and all the other variables and constants on the other side. We will call this solving an equation for a specific variable <em>in general.<\/em> This process is also called <em>solving a literal equation<\/em>. The result is another formula, made up only of variables. The formula contains letters, or <em>literals<\/em>.<\/div>\n<p>Let\u2019s try a few examples, starting with the distance, rate, and time formula we used above.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve the formula [latex]d=rt[\/latex] for [latex]t\\text{:}[\/latex]<\/p>\n<ol>\n<li>When [latex]d=520[\/latex] and [latex]r=65[\/latex]<\/li>\n<li>In general.<\/li>\n<\/ol>\n<p>Solution:<br \/>\nWe\u2019ll write the solutions side-by-side so you can see that solving a formula in general uses the same steps as when we have numbers to substitute.<\/p>\n<table id=\"eip-id1164150753614\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>1. When [latex]d = 520[\/latex] and [latex]r = 65[\/latex]<\/td>\n<td>2. In general<\/td>\n<\/tr>\n<tr>\n<td>Write the formula.<\/td>\n<td>[latex]d=rt[\/latex]<\/td>\n<td>[latex]d=rt[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute any given values.<\/td>\n<td>[latex]520=65t[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Divide to isolate <em>t<\/em>.<\/td>\n<td>[latex]{\\Large\\frac{520}{65}}={\\Large\\frac{65t}{65}}[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{d}{r}}={\\Large\\frac{rt}{r}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]8=t[\/latex][latex]t=8[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{d}{r}}=t[\/latex][latex]t={\\Large\\frac{d}{r}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>We say the formula [latex]t={\\Large\\frac{d}{r}}[\/latex] is solved for [latex]t[\/latex]. We can use this version of the formula any time we are given the distance and rate and need to find the time.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145634\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145634&#38;theme=oea&#38;iframe_resize_id=ohm145634&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The formula [latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex] can be used to find the area of a triangle when given the base and height. In the next example, we will solve this formula for the height.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The formula for area of a triangle is [latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex]. Solve this formula for [latex]h\\text{:}[\/latex]<\/p>\n<ol>\n<li>When [latex]A=90[\/latex] and [latex]b=15[\/latex]<\/li>\n<li>In general<\/li>\n<\/ol>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q190834\">Show Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q190834\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1170572798895\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>1. When <em>A<\/em> = 90 and <em>b<\/em> = 15<\/td>\n<td>2. In general<\/td>\n<\/tr>\n<tr>\n<td>Write the forumla.<\/td>\n<td>[latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex]<\/td>\n<td>[latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute any given values.<\/td>\n<td>[latex]90=\\Large\\frac{1}{2}\\normalsize\\cdot{15}\\cdot{h}[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Clear the fractions.<\/td>\n<td>[latex]\\color{red}{2}\\cdot{90}=\\color{red}{2}\\cdot\\Large\\frac{1}{2}\\normalsize\\cdot{15}\\cdot{h}[\/latex]<\/td>\n<td>[latex]\\color{red}{2}\\cdot{A}=\\color{red}{2}\\cdot\\Large\\frac{1}{2}\\normalsize\\cdot{b}\\cdot{h}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]180=15h[\/latex]<\/td>\n<td>[latex]2A=bh[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Solve for <em>h<\/em>.<\/td>\n<td>[latex]12=h[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{2A}{b}}=h[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We can now find the height of a triangle, if we know the area and the base, by using the formula<\/p>\n<p>[latex]h={\\Large\\frac{2A}{b}}[\/latex]<\/p>\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=\"ohm145635\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145635&#38;theme=oea&#38;iframe_resize_id=ohm145635&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The formula [latex]I=Prt[\/latex] is used to calculate simple interest, where [latex]I[\/latex] is interest, [latex]P[\/latex] is principal, [latex]r[\/latex] is rate as a decimal, and [latex]t[\/latex] is time in years.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve the formula [latex]I=Prt[\/latex] to find the principal, [latex]P\\text{:}[\/latex]<\/p>\n<ol>\n<li>When [latex]I=\\text{\\$5,600},r=\\text{4%},t=7\\text{years}[\/latex]<\/li>\n<li>In general<\/li>\n<\/ol>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q542986\">Show Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q542986\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168058902092\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><em>1. \u00a0I<\/em> = $5600, <em>r<\/em> = 4%, <em>t<\/em> = 7 years<\/td>\n<td>2. In general<\/td>\n<\/tr>\n<tr>\n<td>Write the forumla.<\/td>\n<td>[latex]I=Prt[\/latex]<\/td>\n<td>[latex]I=Prt[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute any given values.<\/td>\n<td>[latex]5600=P(0.04)(7)[\/latex]<\/td>\n<td>[latex]I=Prt[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply <em>r<\/em> \u22c5 <em>t<\/em>.<\/td>\n<td>[latex]5600=P(0.28)[\/latex]<\/td>\n<td>[latex]I=P(rt)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide to isolate <em>P<\/em>.<\/td>\n<td>[latex]\\Large\\frac{5600}{\\color{red}{0.28}}\\normalsize =\\Large\\frac{P(0.28)}{\\color{red}{0.28}}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{I}{\\color{red}{rt}}\\normalsize =\\Large\\frac{P(rt)}{\\color{red}{rt}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]20,000=P[\/latex]<\/td>\n<td>[latex]\\Large\\frac{I}{rt}\\normalsize =P[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>State the answer.<\/td>\n<td>The principal is $20,000.<\/td>\n<td>[latex]P=\\Large\\frac{I}{rt}[\/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=\"ohm145640\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145640&#38;theme=oea&#38;iframe_resize_id=ohm145640&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see another\u00a0example of how to solve an equation for a specific variable.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Find the Base of a Triangle Given Area \/ Literal Equation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/VQZQvJ3rXYg?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>The following examples just ask you to solve a formula in general, without finding particular values.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve the formula [latex]P=a+b+c[\/latex] for [latex]a[\/latex].<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q872233\">Show Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q872233\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe will isolate [latex]a[\/latex] on one side of the equation.<\/p>\n<table id=\"eip-id1168469748609\" class=\"unnumbered unstyled\" summary=\"The top line says,\">\n<tbody>\n<tr>\n<td>We will isolate <em>a<\/em> on one side of the equation.<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write the equation.<\/td>\n<td><\/td>\n<td>[latex]P=a+b+c[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract <em>b<\/em> and <em>c<\/em> from both sides to isolate <em>a<\/em>.<\/td>\n<td><\/td>\n<td>[latex]P\\color{red}{-b-c}=a+b+c\\color{red}{-b-c}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><\/td>\n<td>[latex]P-b-c=a[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>So, [latex]a=P-b-c[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm142894\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142894&#38;theme=oea&#38;iframe_resize_id=ohm142894&#38;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-4221\">\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>Revision and Adaptation. <strong>Provided 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>Find the Base of a Triangle Given Area \/ Literal Equation. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/VQZQvJ3rXYg\">https:\/\/youtu.be\/VQZQvJ3rXYg<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID 142912, 142894, 145640,  145635. <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, 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":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Find the Base of a Triangle Given Area \/ Literal Equation\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/VQZQvJ3rXYg\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"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\":\"cc\",\"description\":\"Question ID 142912, 142894, 145640,  145635\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4221","chapter","type-chapter","status-web-only","hentry"],"part":4179,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4221","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4221\/revisions"}],"predecessor-version":[{"id":4522,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4221\/revisions\/4522"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/4179"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4221\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4221"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4221"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4221"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}