{"id":275662,"date":"2025-07-31T03:31:26","date_gmt":"2025-07-31T03:31:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=275662"},"modified":"2025-07-31T03:31:29","modified_gmt":"2025-07-31T03:31:29","slug":"alina-spent-no-more-than-45-on-gas-for-a-road-trip-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/31\/alina-spent-no-more-than-45-on-gas-for-a-road-trip-3\/","title":{"rendered":"Alina spent no more than $45 on gas for a road trip."},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-1263.png\" alt=\"\" class=\"wp-image-276241\"\/><\/figure>\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>The correct answer is&nbsp;<strong>C. 3.5x + 4y \u2264 45, 0 \u2264 y \u2264 11.25<\/strong>.<\/p>\n\n\n\n<p>Here is a detailed explanation of how to arrive at this answer.<\/p>\n\n\n\n<p>First, we need to translate the word problem into a mathematical inequality. The problem states that Alina spent &#8220;no more than $45&#8221; on gas. The phrase &#8220;no more than&#8221; means the total amount spent must be less than or equal to $45. This gives us the inequality symbol \u2264.<\/p>\n\n\n\n<p>Next, let&#8217;s define the variables and set up an expression for the total cost.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x\u00a0represents the number of gallons of gas bought at the first station. The cost at this station is $3.50 per gallon, so the total amount spent here is\u00a03.50x.<\/li>\n\n\n\n<li>y\u00a0represents the number of gallons of gas bought at the second station. The cost at this station is $4.00 per gallon, so the total amount spent here is\u00a04.00y\u00a0or simply\u00a04y.<\/li>\n<\/ul>\n\n\n\n<p>The total amount Alina spent on gas is the sum of the costs from both stations:&nbsp;3.5x + 4y.<\/p>\n\n\n\n<p>Combining this expression with the spending limit, we get the complete inequality that relates the variables to the total amount paid:<br>3.5x + 4y \u2264 45<\/p>\n\n\n\n<p>This first part of the solution eliminates options A and B, which incorrectly use the \u2265 symbol.<\/p>\n\n\n\n<p>The second part of the question asks for the possible values of&nbsp;y. To find the range for&nbsp;y, we must consider its minimum and maximum possible values based on the inequality and real world constraints.<\/p>\n\n\n\n<p>The minimum value for&nbsp;y&nbsp;is 0. Since&nbsp;y&nbsp;represents the number of gallons of gas, Alina cannot buy a negative amount. The least she could buy from the second station is zero gallons. Therefore,&nbsp;y \u2265 0.<\/p>\n\n\n\n<p>To find the maximum possible value for&nbsp;y, we must consider the scenario where Alina spends as much of her budget as possible on gas from the second station. This happens when she buys the least possible amount of gas from the first station. The minimum amount of gas she can buy from the first station is&nbsp;x = 0&nbsp;gallons.<\/p>\n\n\n\n<p>We can substitute&nbsp;x = 0&nbsp;into our inequality to solve for the maximum value of&nbsp;y:<br>3.5(0) + 4y \u2264 45<br>0 + 4y \u2264 45<br>4y \u2264 45<\/p>\n\n\n\n<p>Now, divide both sides by 4 to isolate&nbsp;y:<br>y \u2264 45 \/ 4<br>y \u2264 11.25<\/p>\n\n\n\n<p>This tells us that the maximum number of gallons Alina can buy from the second station is 11.25.<\/p>\n\n\n\n<p>By combining the minimum (y \u2265 0) and maximum (y \u2264 11.25) values, we find the complete range of possible values for&nbsp;y:<br>0 \u2264 y \u2264 11.25<\/p>\n\n\n\n<p>Therefore, the correct choice must have the inequality&nbsp;3.5x + 4y \u2264 45&nbsp;and the range&nbsp;0 \u2264 y \u2264 11.25. This perfectly matches option C.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2583.jpeg\" alt=\"\" class=\"wp-image-276242\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;C. 3.5x + 4y \u2264 45, 0 \u2264 y \u2264 11.25. Here is a detailed explanation of how to arrive at this answer. First, we need to translate the word problem into a mathematical inequality. The problem states that Alina spent &#8220;no more than $45&#8221; on [&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-275662","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275662","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=275662"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275662\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=275662"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=275662"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=275662"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}