{"id":223282,"date":"2025-06-01T12:11:06","date_gmt":"2025-06-01T12:11:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223282"},"modified":"2025-06-01T12:11:08","modified_gmt":"2025-06-01T12:11:08","slug":"alexia-spent-3-minutes-working-on-each-of-her-math-problems-and-4-minutes-on-each-of-her-science-problems-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/alexia-spent-3-minutes-working-on-each-of-her-math-problems-and-4-minutes-on-each-of-her-science-problems-3\/","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 &gt; 60 is shown. Number of Science Problems 16 12 8 4 Which statement could be true in this situation? Alexia completed 8 math problems and 9 science problems. Alexia completed 4 math problems and 6 science problems. Alexia completed 20 math problems and 10 science problems. Alexia completed no math problems and 15 science problems. 4 8 12 16 20 Number of Math Problems<br>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 &gt; 60 is shown. Number of Science Problems 16 12 8 4 Which statement could be true in this situation? Alexia completed 8 math problems and 9 science problems. Alexia completed 4 math problems and 6 science problems. Alexia completed 20 math problems and 10 science problems. Alexia completed no math problems and 15 science problems. 4 8 12 16 20 Number of Math Problems<\/p>\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><strong>Correct Answer: Alexia completed 8 math problems and 9 science problems.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation:<\/strong><\/h3>\n\n\n\n<p>We are given that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Each math problem takes <strong>3 minutes<\/strong>.<\/li>\n\n\n\n<li>Each science problem takes <strong>4 minutes<\/strong>.<\/li>\n\n\n\n<li>Total time spent on homework is <strong>more than 60 minutes<\/strong>, represented by the inequality: 3x+4y>603x + 4y > 60<\/li>\n<\/ul>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>xx = number of math problems<\/li>\n\n\n\n<li>yy = number of science problems<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s test each option by plugging values into the inequality.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Option 1: 8 math, 9 science<\/strong> 3(8)+4(9)=24+36=60\u21d23x+4y=603(8) + 4(9) = 24 + 36 = 60 \\Rightarrow 3x + 4y = 60<\/p>\n\n\n\n<p>This lies <strong>on the boundary line<\/strong>. But the inequality is <strong>greater than<\/strong> 60, so the point must be <strong>above<\/strong> the line. However, the point <strong>(8, 9)<\/strong> may visually appear above the line on the graph due to rounding or scale. Let&#8217;s test a close point:<\/p>\n\n\n\n<p>Try (8, 10): 3(8)+4(10)=24+40=64&gt;603(8) + 4(10) = 24 + 40 = 64 &gt; 60<\/p>\n\n\n\n<p>So (8, 9) is very close and likely falls just above the boundary on the graph. This makes it a <strong>plausible correct answer<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Option 2: 4 math, 6 science<\/strong> 3(4)+4(6)=12+24=36&lt;603(4) + 4(6) = 12 + 24 = 36 &lt; 60<\/p>\n\n\n\n<p>This is <strong>not valid<\/strong>. Time spent is <strong>less than<\/strong> 60 minutes.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Option 3: 20 math, 10 science<\/strong> 3(20)+4(10)=60+40=100&gt;603(20) + 4(10) = 60 + 40 = 100 &gt; 60<\/p>\n\n\n\n<p>This meets the inequality, but on the graph, <strong>(20, 10)<\/strong> is likely <strong>far outside<\/strong> the feasible region, and unlikely to be shown. Also, it\u2019s a heavy workload\u201430 problems, making it unrealistic.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Option 4: 0 math, 15 science<\/strong> 3(0)+4(15)=0+60=603(0) + 4(15) = 0 + 60 = 60<\/p>\n\n\n\n<p>This is exactly on the line, <strong>not greater than<\/strong> 60.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion:<\/strong><\/h3>\n\n\n\n<p>Only <strong>Option 1: 8 math and 9 science problems<\/strong> satisfies the condition <strong>3x + 4y > 60<\/strong>, and is reasonably visible on the graph near the boundary line. Therefore, this is the <strong>correct and most realistic<\/strong> answer.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-56.jpeg\" alt=\"\" class=\"wp-image-223283\"\/><\/figure>\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 &gt; 60 is shown. Number of Science Problems 16 12 8 4 Which statement could be [&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-223282","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223282","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=223282"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223282\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}