{"id":214255,"date":"2025-05-13T21:21:32","date_gmt":"2025-05-13T21:21:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=214255"},"modified":"2025-05-13T21:21:34","modified_gmt":"2025-05-13T21:21:34","slug":"solve-for-the-missing-amounts-for-the-following-separate-cases","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/13\/solve-for-the-missing-amounts-for-the-following-separate-cases\/","title":{"rendered":"Solve for the missing amounts for the following separate cases"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Solve for the missing amounts for the following separate cases. Case 1 2 3 Sales price per unit $ Variable costs per unit 25 $ 20 45 Contribution margin per unit 15 43 Contribution margin ratio 20%<br>Please help me with show all Calculation thank you<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve for the missing values in the given problem, we will use two main formulas related to contribution margin:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Key Formulas:<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Contribution Margin (CM) per unit = Sales Price per unit \u2212 Variable Cost per unit<\/strong><\/li>\n\n\n\n<li><strong>Contribution Margin Ratio (CM Ratio) = (Contribution Margin per unit \u00f7 Sales Price per unit) \u00d7 100<\/strong><\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">We are given a table with partial data. Let&#8217;s recreate and complete the table step by step.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Case<\/th><th>Sales Price\/Unit<\/th><th>Variable Cost\/Unit<\/th><th>CM\/Unit<\/th><th>CM Ratio<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>?<\/td><td>$25<\/td><td>$15<\/td><td>?<\/td><\/tr><tr><td>2<\/td><td>$20<\/td><td>?<\/td><td>$43<\/td><td>?<\/td><\/tr><tr><td>3<\/td><td>?<\/td><td>$45<\/td><td>?<\/td><td>20%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd37 <strong>Case 1:<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Given:\n<ul class=\"wp-block-list\">\n<li>Variable cost = $25<\/li>\n\n\n\n<li>Contribution margin = $15<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1: Use formula to find sales price:<\/strong> Sales&nbsp;Price=CM+Variable&nbsp;Cost=15+25=$40\\text{Sales Price} = \\text{CM} + \\text{Variable Cost} = 15 + 25 = \\$40<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2: Find CM Ratio:<\/strong> CM&nbsp;Ratio=(1540)\u00d7100=37.5%\\text{CM Ratio} = \\left( \\frac{15}{40} \\right) \\times 100 = 37.5\\%<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <strong>Case 1 Completed:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sales Price: $40<\/li>\n\n\n\n<li>CM Ratio: 37.5%<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd37 <strong>Case 2:<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Given:\n<ul class=\"wp-block-list\">\n<li>Sales Price = $20<\/li>\n\n\n\n<li>CM = $43<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u26a0\ufe0f There\u2019s a <strong>problem<\/strong> here. The contribution margin <strong>cannot be greater than<\/strong> the selling price because: CM=Sales&nbsp;Price\u2212Variable&nbsp;Cost\u21d243=20\u2212Variable&nbsp;Cost\u21d2Variable&nbsp;Cost=\u221223\\text{CM} = \\text{Sales Price} &#8211; \\text{Variable Cost} \\Rightarrow \\text{43} = 20 &#8211; \\text{Variable Cost} \\Rightarrow \\text{Variable Cost} = -23<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A <strong>negative variable cost<\/strong> doesn&#8217;t make sense in this context. So <strong>either the CM or sales price is incorrect<\/strong>. Let&#8217;s assume it&#8217;s a typo, and <strong>Sales Price should be $63<\/strong> (so that CM = $43).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sales Price = $63<\/li>\n\n\n\n<li>CM = $43<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1: Variable Cost = 63 \u2212 43 = $20<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2: CM Ratio = (43 \u00f7 63) \u00d7 100 \u2248 68.25%<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <strong>Case 2 Completed (corrected):<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sales Price: $63<\/li>\n\n\n\n<li>Variable Cost: $20<\/li>\n\n\n\n<li>CM Ratio: 68.25%<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd37 <strong>Case 3:<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Given:\n<ul class=\"wp-block-list\">\n<li>Variable cost = $45<\/li>\n\n\n\n<li>CM Ratio = 20%<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Let <strong>S = sales price<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1: Use CM Ratio formula:<\/strong> CMS=20%=0.20\u21d2CM=0.20S\\frac{\\text{CM}}{\\text{S}} = 20\\% = 0.20 \\Rightarrow \\text{CM} = 0.20S<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But CM = Sales Price \u2212 Variable Cost: 0.20S=S\u221245\u21d2S\u22120.20S=45\u21d20.80S=45\u21d2S=450.80=$56.250.20S = S \u2212 45 \\Rightarrow S \u2212 0.20S = 45 \\Rightarrow 0.80S = 45 \\Rightarrow S = \\frac{45}{0.80} = \\$56.25<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2: CM = 56.25 \u2212 45 = $11.25<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <strong>Case 3 Completed:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sales Price: $56.25<\/li>\n\n\n\n<li>CM: $11.25<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Final Completed Table:<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Case<\/th><th>Sales Price\/Unit<\/th><th>Variable Cost\/Unit<\/th><th>CM\/Unit<\/th><th>CM Ratio<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>$40.00<\/td><td>$25.00<\/td><td>$15.00<\/td><td>37.5%<\/td><\/tr><tr><td>2<\/td><td>$63.00<\/td><td>$20.00<\/td><td>$43.00<\/td><td>68.25%<\/td><\/tr><tr><td>3<\/td><td>$56.25<\/td><td>$45.00<\/td><td>$11.25<\/td><td>20%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 <strong>Explanation (300+ words):<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In cost-volume-profit (CVP) analysis, understanding the relationship between sales price, variable cost, contribution margin (CM), and CM ratio is crucial for pricing, profitability, and break-even analysis.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>contribution margin per unit<\/strong> reflects how much revenue remains after covering variable costs. It is calculated by subtracting the variable cost per unit from the selling price. This leftover amount contributes to covering fixed costs and generating profit. The <strong>contribution margin ratio<\/strong>, expressed as a percentage, represents the proportion of each sales dollar that contributes to fixed costs and profit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In <strong>Case 1<\/strong>, we were provided the variable cost and CM per unit. We simply added them to determine the sales price. Then, dividing CM by the sales price gave us the CM ratio. This scenario shows how changes in pricing or costs directly affect profitability.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Case 2<\/strong> initially posed a challenge: the given CM exceeded the sales price, which is not possible. We corrected the likely typo, assuming the correct sales price was $63. This correction allowed us to accurately back-calculate the variable cost and CM ratio, demonstrating how accuracy in data is critical for valid financial analysis.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In <strong>Case 3<\/strong>, the CM ratio and variable cost were given, requiring a more algebraic approach. Using the CM ratio formula and solving for the unknown sales price highlighted how ratios can help uncover unknown values in cost structures.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Overall, these cases illustrate that by knowing just two of the four components\u2014sales price, variable cost, CM, or CM ratio\u2014we can compute the others. This is particularly valuable for decision-making regarding pricing strategies, cost control, and forecasting profits.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solve for the missing amounts for the following separate cases. Case 1 2 3 Sales price per unit $ Variable costs per unit 25 $ 20 45 Contribution margin per unit 15 43 Contribution margin ratio 20%Please help me with show all Calculation thank you The Correct Answer and Explanation is: To solve for the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-214255","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214255","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=214255"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214255\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=214255"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=214255"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=214255"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}