{"id":500,"date":"2023-02-01T00:04:25","date_gmt":"2023-02-01T00:04:25","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/solving-commission-applications\/"},"modified":"2023-02-01T00:04:25","modified_gmt":"2023-02-01T00:04:25","slug":"solving-commission-applications","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/solving-commission-applications\/","title":{"raw":"Solving Commission Applications","rendered":"Solving Commission Applications"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n \t<li>Calculate sales commission given total purchase price and rate<\/li>\n \t<li>Calculate rate of commission given purchase price and commission earned<\/li>\n<\/ul>\n<\/div>\n<p>Sales people often receive a commission, or percent of total sales, for their sales. Their income may be just the commission they earn, or it may be their commission added to their hourly wages or salary. The commission they earn is calculated as a certain percent of the price of each item they sell. That percent is called the <strong>rate of commission<\/strong>.<\/p>\n\n<div class=\"textbox shaded\">\n<h3>Commission<\/h3>\nA commission is a percentage of total sales as determined by the rate of commission.\n\n[latex]\\text{commission}=\\text{rate of commission}\\cdot \\text{total sales}[\/latex]\n\n<\/div>\nTo find the commission on a sale, multiply the rate of commission by the total sales. Just as we did for computing sales tax, remember to first convert the rate of commission from a percent to a decimal.\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\nHelene is a realtor. She receives [latex]\\text{3%}[\/latex] commission when she sells a house. How much commission will she receive for selling a house that costs [latex]\\text{\\$260,000}?[\/latex]\n\nSolution\n<table id=\"eip-id1168468246173\" class=\"unnumbered unstyled\" summary=\"The figures shows the steps to solving the problem. It shows eight steps. Identify what you are asked to find: What is the commission? Choose a variable to represent it: Let the variable c be equal the commission. Write a sentence that gives the information to find it: The commission is 3% of the price. Translate into an equation: The commission is represented by c. The word 'is' is represented with an equals sign. 3% is written as 0.03. The word 'of' is represented with a multiplication dot. The price, $260,000, is written as 260,000. The equation is c = 0.03 \u00b7 260,000. Simplify: c = 7,800. Change the commission rate to percent form: r = 8.5%. Write a complete sentence that answers the question: Helene will receive a commission of $7,800. Check if this answer is reasonable: Yes. 1% of $260,000 is $2,600, and $7,800 is three times $2,600.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the commission?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]c=[\/latex] the commission.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The commission is [latex]3\\text{%}[\/latex] of the price.<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222029\/CNX_BMath_Figure_06_03_016_img-01.png\" alt=\".\"><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]c=7800[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to percent form.<\/td>\n<td>[latex]r=8.5\\text{%}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check. Is this answer reasonable?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. [latex]1\\text{%}[\/latex] of [latex]\\text{\\$260,000}[\/latex] is [latex]\\text{\\$2,600}[\/latex], and [latex]\\text{\\$7,800}[\/latex] is three times [latex]\\text{\\$2,600}[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>Helene will receive a commission of [latex]\\text{\\$7,800}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[ohm_question]146752[\/ohm_question]\n\n<\/div>\nIn this video, we show another example of how to calculate the amount of commission earned given the rate of commission, and the amount of the sale made.\n\nhttps:\/\/youtu.be\/twARikDLjKg\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\nRikki earned [latex]\\text{\\$87}[\/latex] commission when she sold a [latex]\\text{\\$1,450}[\/latex] stove. What rate of commission did she get?\n[reveal-answer q=\"175751\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"175751\"]\n\nSolution\n<table id=\"eip-id1168468542255\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving the problem. It shows nine steps. Identify what are asked to find: What is the rate of commission? Choose a variable to represent it: Let the variable r be equal to the rate of commission. Write a sentence that gives the information to find it: The commission is what percent of the sale? Translate into an equation: The commission, $87, is written as 87. The word 'is' is represented with an equals sign. The percent is represented by r. The word 'of' is represented with a multiplication dot. The amount of the sale, ,450, is written as 1,450. The equation is 87 is equal to r times 1,450. Divide: 87 divided by 1,450 = 1,450 times r divided by 1,450. Simplify: 0.06 is equal to r. Change to percent form: r is equal to 6%. Write a complete sentence that answers the question: The commission was 6% of the price of the stove. Check if this answer is reasonable: Yes. A 10% commission would have been 45. the $6 commission, $87, is a little more than half of that.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the rate of commission?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]r=[\/latex] the rate of commission.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The commission is what percent of the sale?<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222035\/CNX_BMath_Figure_06_03_017_img-01.png\" alt=\".\"><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]\\Large\\frac{87}{1450}\\normalsize =\\Large\\frac{1450r}{1450}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]0.06=r[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to percent form.<\/td>\n<td>[latex]r=6\\text{%}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if this answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. A [latex]10\\text{%}[\/latex] commission would have been [latex]\\text{\\$145}[\/latex].\n\nThe [latex]6\\text{%}[\/latex] commission, [latex]\\text{\\$87}[\/latex], is a little more than half of that.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The commission was [latex]6\\text{%}[\/latex] of the price of the stove.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[\/hidden-answer]\n\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[ohm_question]146754[\/ohm_question]\n\n<\/div>\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Calculate sales commission given total purchase price and rate<\/li>\n<li>Calculate rate of commission given purchase price and commission earned<\/li>\n<\/ul>\n<\/div>\n<p>Sales people often receive a commission, or percent of total sales, for their sales. Their income may be just the commission they earn, or it may be their commission added to their hourly wages or salary. The commission they earn is calculated as a certain percent of the price of each item they sell. That percent is called the <strong>rate of commission<\/strong>.<\/p>\n<div class=\"textbox shaded\">\n<h3>Commission<\/h3>\n<p>A commission is a percentage of total sales as determined by the rate of commission.<\/p>\n<p>[latex]\\text{commission}=\\text{rate of commission}\\cdot \\text{total sales}[\/latex]<\/p>\n<\/div>\n<p>To find the commission on a sale, multiply the rate of commission by the total sales. Just as we did for computing sales tax, remember to first convert the rate of commission from a percent to a decimal.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Helene is a realtor. She receives [latex]\\text{3%}[\/latex] commission when she sells a house. How much commission will she receive for selling a house that costs [latex]\\text{\\$260,000}?[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468246173\" class=\"unnumbered unstyled\" summary=\"The figures shows the steps to solving the problem. It shows eight steps. Identify what you are asked to find: What is the commission? Choose a variable to represent it: Let the variable c be equal the commission. Write a sentence that gives the information to find it: The commission is 3% of the price. Translate into an equation: The commission is represented by c. The word 'is' is represented with an equals sign. 3% is written as 0.03. The word 'of' is represented with a multiplication dot. The price, $260,000, is written as 260,000. The equation is c = 0.03 \u00b7 260,000. Simplify: c = 7,800. Change the commission rate to percent form: r = 8.5%. Write a complete sentence that answers the question: Helene will receive a commission of $7,800. Check if this answer is reasonable: Yes. 1% of $260,000 is $2,600, and $7,800 is three times $2,600.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the commission?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]c=[\/latex] the commission.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The commission is [latex]3\\text{%}[\/latex] of the price.<\/td>\n<\/tr>\n<tr>\n<td>Translate into 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\/24222029\/CNX_BMath_Figure_06_03_016_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]c=7800[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to percent form.<\/td>\n<td>[latex]r=8.5\\text{%}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check. Is this answer reasonable?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. [latex]1\\text{%}[\/latex] of [latex]\\text{\\$260,000}[\/latex] is [latex]\\text{\\$2,600}[\/latex], and [latex]\\text{\\$7,800}[\/latex] is three times [latex]\\text{\\$2,600}[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>Helene will receive a commission of [latex]\\text{\\$7,800}[\/latex].<\/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=\"ohm146752\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146752&theme=oea&iframe_resize_id=ohm146752&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In this video, we show another example of how to calculate the amount of commission earned given the rate of commission, and the amount of the sale made.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Percent Application - Commission Amount Given Percent of Sales (Equation and Proportion)\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/twARikDLjKg?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Rikki earned [latex]\\text{\\$87}[\/latex] commission when she sold a [latex]\\text{\\$1,450}[\/latex] stove. What rate of commission did she get?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q175751\">Show Solution<\/span><\/p>\n<div id=\"q175751\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468542255\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving the problem. It shows nine steps. Identify what are asked to find: What is the rate of commission? Choose a variable to represent it: Let the variable r be equal to the rate of commission. Write a sentence that gives the information to find it: The commission is what percent of the sale? Translate into an equation: The commission, $87, is written as 87. The word 'is' is represented with an equals sign. The percent is represented by r. The word 'of' is represented with a multiplication dot. The amount of the sale, ,450, is written as 1,450. The equation is 87 is equal to r times 1,450. Divide: 87 divided by 1,450 = 1,450 times r divided by 1,450. Simplify: 0.06 is equal to r. Change to percent form: r is equal to 6%. Write a complete sentence that answers the question: The commission was 6% of the price of the stove. Check if this answer is reasonable: Yes. A 10% commission would have been 45. the $6 commission, $87, is a little more than half of that.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the rate of commission?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]r=[\/latex] the rate of commission.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The commission is what percent of the sale?<\/td>\n<\/tr>\n<tr>\n<td>Translate into 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\/24222035\/CNX_BMath_Figure_06_03_017_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]\\Large\\frac{87}{1450}\\normalsize =\\Large\\frac{1450r}{1450}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]0.06=r[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to percent form.<\/td>\n<td>[latex]r=6\\text{%}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if this answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. A [latex]10\\text{%}[\/latex] commission would have been [latex]\\text{\\$145}[\/latex].<\/p>\n<p>The [latex]6\\text{%}[\/latex] commission, [latex]\\text{\\$87}[\/latex], is a little more than half of that.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The commission was [latex]6\\text{%}[\/latex] of the price of the stove.<\/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=\"ohm146754\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146754&theme=oea&iframe_resize_id=ohm146754&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-500\">\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 146754, 146752. <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: Percent Application - Commission Amount Given Percent of Sales (Equation and Proportion). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/twARikDLjKg\">https:\/\/youtu.be\/twARikDLjKg<\/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":538461,"menu_order":6,"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 146754, 146752\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Percent Application - Commission Amount Given Percent of Sales (Equation and Proportion)\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/twARikDLjKg\",\"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-500","chapter","type-chapter","status-publish","hentry"],"part":487,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/500","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/users\/538461"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/500\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/parts\/487"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/500\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/media?parent=500"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=500"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/contributor?post=500"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/license?post=500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}