Let the price at both merchants C and D be $64.95<\/strong>.<\/p>\n\n\n\n Step 1: Find D\u2019s sale price after 20% discount<\/strong> Step 2: Calculate what percentage discount C must offer to reach $51.96<\/strong><\/p>\n\n\n\n Let x<\/strong> be the discount rate C must offer.<\/p>\n\n\n\n Then:<\/p>\n\n\n\n 64.95 \u00d7 (1 – x) = 51.96<\/p>\n<\/blockquote>\n\n\n\n Solving for x<\/strong>:<\/p>\n\n\n\n 1 – x = 51.96 \/ 64.95 Answer: 20%<\/strong><\/p>\n\n\n\n This case is symmetric.<\/p>\n\n\n\n Step 1: Find C\u2019s sale price after 20% discount<\/strong> Step 2: Calculate what discount rate D must give to reach $51.96<\/strong><\/p>\n\n\n\n Let y<\/strong> be the discount rate for D:<\/p>\n\n\n\n 64.95 \u00d7 (1 – y) = 51.96 Answer: 20%<\/strong><\/p>\n\n\n\n When two merchants offer the same original price for a product and each commits to matching the other’s prices, understanding discount equivalency becomes important. If one seller, say Merchant D, runs a 20% off sale, the competitor, Merchant C, must determine the precise percentage discount required to match that reduced price.<\/p>\n\n\n\n A 20% discount on the original price of $64.95 lowers the cost to $51.96. For Merchant C to match this sale price, a customer should be able to buy the product for the same $51.96 from Merchant C. To calculate the necessary discount, compare the reduced price with the original. The fraction of the original price that remains after a 20% discount is 0.80. Multiplying the original price by 0.80 yields $51.96, confirming that a 20% markdown gives the intended result.<\/p>\n\n\n\n Reversing roles, if Merchant C offers a 20% discount, the sale price again becomes $51.96. Merchant D would then also need to offer a 20% discount to match this price. The calculations work identically because the original price is the same for both sellers, and the percentage discount applies uniformly.<\/p>\n\n\n\n Therefore, in both situations, the discount rate required to match a competitor\u2019s 20% sale is exactly 20%. This symmetrical result underscores a fundamental property of percentages when starting from identical values. The matching discount does not need special adjustment or conversion\u2014only replication of the same percentage reduction from the original.<\/p>\n\n\n\n Merchants C and D sell the same article at64.95, respectively. They both advertise that they will match the price offered by any other store on any product that they stock. a. What discount rate must C give to match D’s price marked down by 20% during a sale? b. What discount rate must D give […]<\/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-235994","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235994","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=235994"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235994\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235994"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235994"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235994"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\na. Discount rate C must give to match D’s price after a 20% markdown<\/strong><\/h3>\n\n\n\n
D’s sale price = 64.95 \u00d7 (1 – 0.20)
= 64.95 \u00d7 0.80
= $51.96<\/strong><\/p>\n\n\n\n\n
1 – x \u2248 0.8
x \u2248 0.2 or 20%<\/strong><\/p>\n\n\n\n
\n\n\n\nb. Discount rate D must give to match C’s price after a 20% markdown<\/strong><\/h3>\n\n\n\n
C’s sale price = 64.95 \u00d7 0.80 = $51.96<\/strong><\/p>\n\n\n\n
1 – y = 0.8
y = 0.2 or 20%<\/strong><\/p>\n\n\n\n
\n\n\n\nExplanation (300 words)<\/h3>\n\n\n\n
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