{"id":233605,"date":"2025-06-13T08:52:29","date_gmt":"2025-06-13T08:52:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233605"},"modified":"2025-06-13T08:52:32","modified_gmt":"2025-06-13T08:52:32","slug":"aaden-wants-to-get-a-subscription-to-an-online-library-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/aaden-wants-to-get-a-subscription-to-an-online-library-3\/","title":{"rendered":"Aaden wants to get a subscription to an online library."},"content":{"rendered":"\n<p>Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed 96 dollar annual fee and the other which charges 3 dollars per book he borrows. Here&#8217;s a graph that shows a system of equations for this scenario where<br>is the number of books Aaden borrows and<br>is the total cost of the subscription.<\/p>\n\n\n\n<p><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>To determine which subscription is more cost-effective for Aaden, we analyze the two pricing models:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Plan A (Fixed Plan)<\/strong>: $96 annual fee, regardless of how many books he borrows.<br>This can be represented by the equation:<br><strong>C = 96<\/strong>,<br>where <em>C<\/em> is the total cost, and it does not depend on the number of books borrowed.<\/li>\n\n\n\n<li><strong>Plan B (Per-Book Plan)<\/strong>: No annual fee, but charges $3 for each book borrowed.<br>This is represented by the equation:<br><strong>C = 3b<\/strong>,<br>where <em>C<\/em> is the total cost, and <em>b<\/em> is the number of books borrowed.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Solving the System of Equations:<\/h3>\n\n\n\n<p>We set the two cost equations equal to find the <strong>break-even point<\/strong> \u2014 the number of books for which both plans cost the same: 96=3b96 = 3b96=3b<\/p>\n\n\n\n<p>Divide both sides by 3: b=32b = 32b=32<\/p>\n\n\n\n<p>So, at <strong>32 books<\/strong>, both plans cost <strong>$96<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Interpreting the Graph:<\/h3>\n\n\n\n<p>On the graph:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>horizontal axis<\/strong> represents the number of books borrowed (<em>b<\/em>).<\/li>\n\n\n\n<li>The <strong>vertical axis<\/strong> represents the total cost (<em>C<\/em>).<\/li>\n\n\n\n<li>The line <strong>C = 96<\/strong> is a <strong>horizontal line<\/strong>, showing the fixed cost plan.<\/li>\n\n\n\n<li>The line <strong>C = 3b<\/strong> is a <strong>straight line through the origin<\/strong>, increasing with the number of books.<\/li>\n<\/ul>\n\n\n\n<p>The point where the lines intersect is at <strong>(32, 96)<\/strong>. This is the break-even point.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Decision:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If Aaden borrows <strong>fewer than 32 books<\/strong>, the <strong>$3 per book plan<\/strong> (Plan B) is cheaper.<\/li>\n\n\n\n<li>If Aaden borrows <strong>more than 32 books<\/strong>, the <strong>$96 flat fee plan<\/strong> (Plan A) saves money.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>Aaden should consider how many books he plans to borrow in a year. If it&#8217;s fewer than 32, he saves money with the per-book plan. If it&#8217;s more than 32, the fixed annual subscription is a better choice. This comparison helps make cost-effective decisions using linear equations and graphical interpretation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-281.jpeg\" alt=\"\" class=\"wp-image-233606\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed 96 dollar annual fee and the other which charges 3 dollars per book he borrows. Here&#8217;s a graph that shows a system of equations for this scenario whereis the number of books Aaden borrows [&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-233605","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233605","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=233605"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233605\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233605"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233605"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233605"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}