{"id":150625,"date":"2024-10-09T07:00:13","date_gmt":"2024-10-09T07:00:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=150625"},"modified":"2024-10-09T07:00:17","modified_gmt":"2024-10-09T07:00:17","slug":"alexia-spent-3-minutes-working-on-each-of-her-math-problems-and-4-minutes-on-each-of-her-science-problems","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/09\/alexia-spent-3-minutes-working-on-each-of-her-math-problems-and-4-minutes-on-each-of-her-science-problems\/","title":{"rendered":"Alexia spent 3 minutes working on each of her math problems and 4 minutes on each of her science problems."},"content":{"rendered":"\n<p>Alexia spent 3 minutes working on each of her math problems and 4 minutes on each of her science problems. Her homework took her more than 60 minutes to complete. The boundary line for the inequality 3x + 4y > 60 is shown.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve the inequality involving Alexia&#8217;s homework, we need to establish an equation that represents the problem and determine the correct interpretation of the boundary line.<\/p>\n\n\n\n<p>The key variables are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( x ) represents the number of math problems Alexia worked on.<\/li>\n\n\n\n<li>( y ) represents the number of science problems Alexia worked on.<\/li>\n<\/ul>\n\n\n\n<p>The time Alexia spent on each math problem is 3 minutes, and the time she spent on each science problem is 4 minutes. According to the problem, the total time she spent on both types of problems exceeded 60 minutes. This leads us to the inequality:<\/p>\n\n\n\n<p>[<br>3x + 4y &gt; 60<br>]<\/p>\n\n\n\n<p>This inequality means that the combined time spent on ( x ) math problems and ( y ) science problems must be greater than 60 minutes. The boundary line for this inequality is the equation:<\/p>\n\n\n\n<p>[<br>3x + 4y = 60<br>]<\/p>\n\n\n\n<p>The boundary line represents the exact scenario where Alexia spent exactly 60 minutes on her homework. For any values of ( x ) and ( y ) that fall on the boundary line, the total time spent is exactly 60 minutes. For values above the line, the total time is greater than 60 minutes, satisfying the original inequality ( 3x + 4y &gt; 60 ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Interpretation of the Boundary Line<\/h3>\n\n\n\n<p>The inequality symbol &#8220;&gt;&#8221; implies that we are interested in the region above the boundary line. In a graph, this would represent the area where the combination of math and science problems results in a total time greater than 60 minutes.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Testing Solutions<\/h3>\n\n\n\n<p>To find a valid solution, let\u2019s test a point above the line. For example, if Alexia worked on 10 math problems and 10 science problems:<\/p>\n\n\n\n<p>[<br>3(10) + 4(10) = 30 + 40 = 70<br>]<\/p>\n\n\n\n<p>Since 70 is greater than 60, the point ( (10, 10) ) satisfies the inequality.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The boundary line equation ( 3x + 4y = 60 ) is the dividing line between solutions where Alexia\u2019s homework took exactly 60 minutes and those where it took more than 60 minutes. The correct answer lies in the region above this line, where the inequality ( 3x + 4y &gt; 60 ) is true, meaning her homework took more than 60 minutes.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alexia spent 3 minutes working on each of her math problems and 4 minutes on each of her science problems. Her homework took her more than 60 minutes to complete. The boundary line for the inequality 3x + 4y > 60 is shown. The correct Answer and Explanation is: To solve the inequality involving Alexia&#8217;s [&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-150625","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150625","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=150625"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150625\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150625"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}