{"id":153879,"date":"2024-10-13T19:01:35","date_gmt":"2024-10-13T19:01:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=153879"},"modified":"2024-10-13T19:01:37","modified_gmt":"2024-10-13T19:01:37","slug":"alina-spent-no-more-than-45-on-gas-for-a-road-trip","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/13\/alina-spent-no-more-than-45-on-gas-for-a-road-trip\/","title":{"rendered":"Alina spent no more than $45 on gas for a road trip"},"content":{"rendered":"\n<p>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.<br>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,<br>and the total amount she paid? what are the possible values of y?<br>A. 3.5x 4y = 45, y = 11.25<br>B. 3.5x 4y = 45, 0 = y = 10.375<br>C. 3.5x 4y = 45, 0 = y = 11.25<br>D. 3.5x 4y = 45, y = 10.375<\/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 find the correct inequality and possible values of ( y ), we first need to represent the total cost of gas purchased from two different gas stations.<\/p>\n\n\n\n<p>Let:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( x ) = the number of gallons of gas bought at the first station (which charges $3.50 per gallon)<\/li>\n\n\n\n<li>( y ) = the number of gallons of gas bought at the second station (which charges $4.00 per gallon)<\/li>\n<\/ul>\n\n\n\n<p>The total cost ( C ) can be expressed as:<br>[<br>C = 3.50x + 4.00y<br>]<\/p>\n\n\n\n<p>Since Alina spent no more than $45 on gas, we can write the inequality as:<br>[<br>3.50x + 4.00y \\leq 45<br>]<\/p>\n\n\n\n<p>Now, to analyze the possible values of ( y ), we will isolate ( y ) in the inequality:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Rearranging the inequality gives us:<br>[<br>4.00y \\leq 45 &#8211; 3.50x<br>]<br>[<br>y \\leq \\frac{45 &#8211; 3.50x}{4}<br>]<\/li>\n<\/ol>\n\n\n\n<p>Next, we need to determine the maximum value of ( y ) when ( x = 0 ) (i.e., when all the gas is purchased from the second station):<br>[<br>y \\leq \\frac{45 &#8211; 3.50(0)}{4} = \\frac{45}{4} = 11.25<br>]<\/p>\n\n\n\n<p>This indicates that ( y ) can take any value from ( 0 ) to ( 11.25 ), provided that the total cost does not exceed $45.<\/p>\n\n\n\n<p>Now, let&#8217;s summarize the options provided:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A. ( 3.5x + 4y = 45, y = 11.25 )<\/li>\n\n\n\n<li>B. ( 3.5x + 4y = 45, 0 \\leq y \\leq 10.375 )<\/li>\n\n\n\n<li>C. ( 3.5x + 4y = 45, 0 \\leq y \\leq 11.25 )<\/li>\n\n\n\n<li>D. ( 3.5x + 4y = 45, y = 10.375 )<\/li>\n<\/ul>\n\n\n\n<p>Given our analysis, the correct option is:<br><strong>C. ( 3.5x + 4y = 45, 0 \\leq y \\leq 11.25 )<\/strong><\/p>\n\n\n\n<p>This option correctly reflects the total cost equation and the range of values for ( y ), which indicates that Alina can purchase up to 11.25 gallons of gas from the second station without exceeding her budget. Thus, as long as ( y ) remains within this interval, the inequality holds true, allowing Alina to manage her expenses efficiently on her road trip.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>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 [&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-153879","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153879","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=153879"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153879\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=153879"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=153879"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=153879"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}