{"id":277471,"date":"2025-08-01T07:03:03","date_gmt":"2025-08-01T07:03:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=277471"},"modified":"2025-08-01T07:03:06","modified_gmt":"2025-08-01T07:03:06","slug":"alexia-spent-3-minutes-working-on-each-of-her-math-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/01\/alexia-spent-3-minutes-working-on-each-of-her-math-2\/","title":{"rendered":"Alexia spent 3 minutes working on each of her math"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-15.png\" alt=\"\" class=\"wp-image-277472\"\/><\/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>Alexia completed 20 math problems and 10 science problems.<\/strong><\/p>\n\n\n\n<p>Here is a detailed explanation of the solution.<\/p>\n\n\n\n<p>The problem asks to identify a situation that could be true based on the given information. The information states that Alexia spent 3 minutes on each math problem and 4 minutes on each science problem, and her total homework time was &#8220;more than 60 minutes.&#8221;<\/p>\n\n\n\n<p>First, let&#8217;s represent this situation with a mathematical inequality. Let&nbsp;x&nbsp;be the number of math problems and&nbsp;y&nbsp;be the number of science problems. The total time spent on math is&nbsp;3x&nbsp;minutes, and the total time spent on science is&nbsp;4y&nbsp;minutes. The total time for all homework is the sum of these two,&nbsp;3x + 4y. Since the problem states this total time was &#8220;more than 60 minutes,&#8221; the correct inequality is&nbsp;3x + 4y &gt; 60.<\/p>\n\n\n\n<p>The graph provided shows a dashed boundary line for the equation&nbsp;3x + 4y = 60. A dashed line signifies a strict inequality (&gt;&nbsp;or&nbsp;&lt;), meaning that any combination of problems that falls directly on the line is not a valid solution. A valid solution must be a point in the region above this line.<\/p>\n\n\n\n<p>Now, we can test each of the given options by plugging the values of&nbsp;x&nbsp;(math problems) and&nbsp;y&nbsp;(science problems) into our inequality&nbsp;3x + 4y &gt; 60.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Option 1:<\/strong>\u00a08 math problems and 9 science problems.\n<ul class=\"wp-block-list\">\n<li>x = 8,\u00a0y = 9<\/li>\n\n\n\n<li>3(8) + 4(9) = 24 + 36 = 60.<\/li>\n\n\n\n<li>This results in\u00a060 > 60, which is false. This point lies on the boundary line, so it is not a solution.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Option 2:<\/strong>\u00a04 math problems and 6 science problems.\n<ul class=\"wp-block-list\">\n<li>x = 4,\u00a0y = 6<\/li>\n\n\n\n<li>3(4) + 4(6) = 12 + 24 = 36.<\/li>\n\n\n\n<li>This results in\u00a036 > 60, which is false. This amount of work took less than 60 minutes.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Option 3:<\/strong>\u00a020 math problems and 10 science problems.\n<ul class=\"wp-block-list\">\n<li>x = 20,\u00a0y = 10<\/li>\n\n\n\n<li>3(20) + 4(10) = 60 + 40 = 100.<\/li>\n\n\n\n<li>This results in\u00a0100 > 60, which is true. This combination of problems takes more than 60 minutes and is a valid solution.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Option 4:<\/strong>\u00a0no math problems and 15 science problems.\n<ul class=\"wp-block-list\">\n<li>x = 0,\u00a0y = 15<\/li>\n\n\n\n<li>3(0) + 4(15) = 0 + 60 = 60.<\/li>\n\n\n\n<li>This results in\u00a060 > 60, which is false. This point is the y-intercept of the boundary line and is not a solution.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the only statement that could be true is the one where Alexia completed 20 math problems and 10 science problems, as it is the only option that results in a total time greater than 60 minutes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner6-17.jpeg\" alt=\"\" class=\"wp-image-277473\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is:&nbsp;Alexia completed 20 math problems and 10 science problems. Here is a detailed explanation of the solution. The problem asks to identify a situation that could be true based on the given information. The information states that Alexia spent 3 minutes on each math problem and [&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-277471","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277471","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=277471"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277471\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=277471"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=277471"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=277471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}