{"id":186033,"date":"2025-01-24T04:39:14","date_gmt":"2025-01-24T04:39:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186033"},"modified":"2025-01-24T04:39:16","modified_gmt":"2025-01-24T04:39:16","slug":"gina-chuez-has-considered-starting-her-own-custom-greeting-card-business","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/24\/gina-chuez-has-considered-starting-her-own-custom-greeting-card-business\/","title":{"rendered":"Gina Chuez has considered starting her own custom greeting card business"},"content":{"rendered":"\n<p>Gina Chuez has considered starting her own custom greeting card business. With an initial start-up cost of $1500, she figures it will cost $0.45 to produce each card. In order to remain competitive with the larger greeting card companies, Gina must sell her cards for no more than $1.70 each. To make a profit, her income must exceed her costs. How many cards must she sell before making a profit?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine how many cards Gina must sell to make a profit, we need to set up an equation for her costs and income.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Define variables<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let ( x ) be the number of cards Gina sells.<\/li>\n\n\n\n<li>The cost to produce each card is $0.45, so the total cost to produce ( x ) cards is ( 0.45x ).<\/li>\n\n\n\n<li>The initial start-up cost is $1500.<\/li>\n\n\n\n<li>The revenue she gets from selling each card is $1.70, so her total revenue from selling ( x ) cards is ( 1.70x ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Write the profit condition<\/h3>\n\n\n\n<p>Gina makes a profit when her income (revenue) exceeds her costs. This can be written as:<br>[<br>\\text{Income} &gt; \\text{Costs}<br>]<br>The total income is ( 1.70x ), and the total cost is ( 1500 + 0.45x ) (the initial cost plus the production cost per card). So the inequality becomes:<br>[<br>1.70x &gt; 1500 + 0.45x<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solve the inequality<\/h3>\n\n\n\n<p>To solve for ( x ), subtract ( 0.45x ) from both sides of the inequality:<br>[<br>1.70x &#8211; 0.45x &gt; 1500<br>]<br>[<br>1.25x &gt; 1500<br>]<\/p>\n\n\n\n<p>Now, divide both sides by 1.25 to isolate ( x ):<br>[<br>x &gt; \\frac{1500}{1.25}<br>]<br>[<br>x &gt; 1200<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Conclusion<\/h3>\n\n\n\n<p>Gina must sell <strong>at least 1201 cards<\/strong> to make a profit. This is because she needs to sell more than 1200 cards, and since the number of cards sold must be a whole number, 1201 cards is the minimum number that will result in a profit.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The start-up cost of $1500 is a fixed cost, and each card produced costs $0.45 to make. To make a profit, the income from selling the cards must exceed both the start-up cost and the production cost. By solving the inequality, we found that selling 1201 cards will ensure that Gina&#8217;s income exceeds her total costs, which means she will make a profit.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Gina Chuez has considered starting her own custom greeting card business. With an initial start-up cost of $1500, she figures it will cost $0.45 to produce each card. In order to remain competitive with the larger greeting card companies, Gina must sell her cards for no more than $1.70 each. To make a profit, her [&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-186033","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186033","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=186033"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186033\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186033"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186033"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}