{"id":217404,"date":"2025-05-21T20:15:19","date_gmt":"2025-05-21T20:15:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=217404"},"modified":"2025-05-21T20:15:21","modified_gmt":"2025-05-21T20:15:21","slug":"the-car-rental-agency-charges-a-flat-rate-of-60-plus-0-50-per-mile-for-every-mile-she-drives-over-40-miles","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/21\/the-car-rental-agency-charges-a-flat-rate-of-60-plus-0-50-per-mile-for-every-mile-she-drives-over-40-miles\/","title":{"rendered":"The car rental agency charges a flat rate of $60 plus $0.50 per mile for every mile she drives over 40 miles."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"> The car rental agency charges a flat rate of $60 plus $0.50 per mile for every mile she drives over 40 miles. Stella&#8217;s company will pay up to $270, excluding the cost of gasoline, for the use of the rental car. What is the greatest number of miles Stella can drive the rental car without spending more than $270?<\/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-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s break down the problem step-by-step:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem Recap:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Flat rental fee: $60 (this covers up to 40 miles).<\/li>\n\n\n\n<li>Additional charge: $0.50 per mile <strong>over 40 miles<\/strong>.<\/li>\n\n\n\n<li>Maximum amount the company will pay: $270.<\/li>\n\n\n\n<li>Gasoline cost is excluded, so we only consider the rental charges.<\/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\">What is asked?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Find the greatest number of miles Stella can drive without the total rental cost exceeding $270.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Define the variables<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let xx = total miles driven.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Write the cost function<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first 40 miles cost a flat $60.<\/li>\n\n\n\n<li>For every mile over 40, charge is $0.50 per mile.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">If Stella drives xx miles and x&gt;40x &gt; 40, the extra miles are x\u221240x &#8211; 40.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, total cost CC is: C=60+0.50(x\u221240)C = 60 + 0.50(x &#8211; 40)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Set up inequality<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The company will pay <strong>up to<\/strong> $270, so: 60+0.50(x\u221240)\u226427060 + 0.50(x &#8211; 40) \\leq 270<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Solve the inequality<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">60+0.50(x\u221240)\u226427060 + 0.50(x &#8211; 40) \\leq 270<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Subtract 60 from both sides: 0.50(x\u221240)\u22642100.50(x &#8211; 40) \\leq 210<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Multiply both sides by 2 (to clear the 0.5): x\u221240\u2264420x &#8211; 40 \\leq 420<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Add 40 to both sides: x\u2264460x \\leq 460<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Interpretation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Stella can drive <strong>up to 460 miles<\/strong> without exceeding the $270 limit.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>460 miles<\/strong> is the greatest number of miles Stella can drive without spending more than $270.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This problem involves a fixed base fee plus a variable cost depending on the miles driven beyond a threshold. The flat fee ($60) covers the first 40 miles regardless of the actual distance up to that point. Beyond 40 miles, the rental agency charges $0.50 per mile.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the maximum number of miles Stella can drive without exceeding $270, we model the cost as the sum of the flat rate and the variable charge for miles exceeding 40.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Setting this sum less than or equal to the company\u2019s maximum payment limit, we solve for the miles. By isolating xx, the total miles driven, the calculation shows that Stella can drive up to 460 miles before costs exceed $270.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This approach is typical of piecewise linear cost problems where a base charge covers an initial quantity and additional fees apply beyond that. This method ensures Stella stays within her company\u2019s reimbursement limit while maximizing her mileage.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">If you want, I can also explain how this would be visualized on a graph or provide a real-world example for better understanding!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The car rental agency charges a flat rate of $60 plus $0.50 per mile for every mile she drives over 40 miles. Stella&#8217;s company will pay up to $270, excluding the cost of gasoline, for the use of the rental car. What is the greatest number of miles Stella can drive the rental car without [&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-217404","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217404","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=217404"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217404\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217404"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217404"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}