{"id":222868,"date":"2025-06-01T04:01:58","date_gmt":"2025-06-01T04:01:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=222868"},"modified":"2025-06-01T04:02:00","modified_gmt":"2025-06-01T04:02:00","slug":"alina-spent-no-more-than-45-on-gas-for-a-road-trip-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/alina-spent-no-more-than-45-on-gas-for-a-road-trip-2\/","title":{"rendered":"Alina spent no more than $45 on gas for a road trip"},"content":{"rendered":"\n

Alina spent no more than $45 on gas for a road trip. The first gas station she used charged $3.50 per gallon and the second gas station charged $4.00 per gallon. Which inequality relates the number of gallons of gas she bought at the first station, x, the number of gallons of gas she bought at the second station, y, and the total amount she paid? What are the possible values of y? Answers: A) 3.5x + 4y \u00e2\u2030\u00a5 45, y \u00e2\u2030\u00a5 11.25 B) 3.5x + 4y \u00e2\u2030\u00a5 45, 0 \u00e2\u2030\u00a4 y \u00e2\u2030\u00a4 10.375 C) 3.5x + 4y \u00e2\u2030\u00a4 45, 0 \u00e2\u2030\u00a4 y \u00e2\u2030\u00a4 11.25 D) 3.5x + 4y \u00e2\u2030\u00a4 45, y \u00e2\u2030\u00a5 10.375
Alina spent no more than
3.50 per gallon and the second gas station charged $4.00 per gallon. Which inequality relates the number of gallons of gas she bought at the first station, x, the number of gallons of gas she bought at the second station, y, and the total amount she paid? What are the possible values of y? Answers: A) 3.5x + 4y \u00e2\u2030\u00a5 45, y \u00e2\u2030\u00a5 11.25 B) 3.5x + 4y \u00e2\u2030\u00a5 45, 0 \u00e2\u2030\u00a4 y \u00e2\u2030\u00a4 10.375 C) 3.5x + 4y \u00e2\u2030\u00a4 45, 0 \u00e2\u2030\u00a4 y \u00e2\u2030\u00a4 11.25 D) 3.5x + 4y \u00e2\u2030\u00a4 45, y \u00e2\u2030\u00a5 10.375<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer: C) 3.5x + 4y \u2264 45, 0 \u2264 y \u2264 11.25<\/strong><\/p>\n\n\n\n

Explanation:<\/strong><\/h3>\n\n\n\n

Alina is taking a road trip and bought gas at two gas stations<\/strong>. The first station charges $3.50 per gallon<\/strong>, and the second charges $4.00 per gallon<\/strong>. She spent no more than $45 in total<\/strong>. Let:<\/p>\n\n\n\n

    \n
  • xx = gallons purchased at the first station<\/li>\n\n\n\n
  • yy = gallons purchased at the second station<\/li>\n<\/ul>\n\n\n\n

    The total cost of the gas she purchased is: 3.5x+4y3.5x + 4y<\/p>\n\n\n\n

    Because she spent no more than $45<\/strong>, this total must be less than or equal to 45<\/strong>: 3.5x+4y\u2264453.5x + 4y \\leq 45<\/p>\n\n\n\n

    This inequality expresses the constraint on her total spending. Any solution (x,y)(x, y) that satisfies this inequality is a possible combination of gallons bought from both stations without exceeding her $45 budget.<\/p>\n\n\n\n

    Now, we determine the possible values of yy (gallons bought at the second station). Since gas at the second station costs more ($4.00), to find the maximum<\/strong> she could have bought there if she bought only from that station<\/strong>, set x=0x = 0: 3.5(0)+4y\u226445\u21d24y\u226445\u21d2y\u2264454=11.253.5(0) + 4y \\leq 45 \\Rightarrow 4y \\leq 45 \\Rightarrow y \\leq \\frac{45}{4} = 11.25<\/p>\n\n\n\n

    This means the maximum value of yy<\/strong> is 11.25<\/strong>, and since she can\u2019t buy negative gallons, the minimum is 0<\/strong>. So: 0\u2264y\u226411.250 \\leq y \\leq 11.25<\/p>\n\n\n\n

    Why Option C is Correct:<\/strong><\/h3>\n\n\n\n
      \n
    • It correctly uses the inequality 3.5x+4y\u2264453.5x + 4y \\leq 45<\/strong> to reflect the budget limit.<\/li>\n\n\n\n
    • It correctly identifies the possible values of yy: from 0 to 11.25 gallons<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Why Other Options Are Incorrect:<\/strong><\/h3>\n\n\n\n
        \n
      • A and B<\/strong> use the wrong inequality sign (\u2265 45<\/strong>), which contradicts \u201cno more than $45.\u201d<\/li>\n\n\n\n
      • D<\/strong> has the correct inequality but says y\u226510.375y \\geq 10.375<\/strong>, which wrongly restricts minimum y.<\/li>\n<\/ul>\n\n\n\n

        \u2705 Final Answer: C.<\/strong><\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Alina spent no more than $45 on gas for a road trip. The first gas station she used charged $3.50 per gallon and the second gas station charged $4.00 per gallon. Which inequality relates the number of gallons of gas she bought at the first station, x, the number of gallons of gas she bought […]<\/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-222868","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222868","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=222868"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222868\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=222868"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=222868"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=222868"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}