{"id":223285,"date":"2025-06-01T12:17:12","date_gmt":"2025-06-01T12:17:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223285"},"modified":"2025-06-01T12:17:19","modified_gmt":"2025-06-01T12:17:19","slug":"alexia-spent-3-minutes-working-on-each-of-her-math-problems-and-4-minutes-on-each-of-her-science-problems-4","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-4\/","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. 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><\/p>\n\n\n\n<p> <\/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>The correct answer is: <strong>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 the inequality: 3x+4y&gt;603x + 4y &gt; 60<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>xx = number of <strong>math problems<\/strong> (3 minutes each)<\/li>\n\n\n\n<li>yy = number of <strong>science problems<\/strong> (4 minutes each)<\/li>\n<\/ul>\n\n\n\n<p>This inequality represents the condition that <strong>Alexia spent more than 60 minutes on homework<\/strong>. We are to test which option satisfies this condition.<\/p>\n\n\n\n<p>Let\u2019s plug each choice into the inequality:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Option A:<\/strong> 8 math, 9 science 3(8)+4(9)=24+36=60\u2192&nbsp;Not&nbsp;greater&nbsp;than&nbsp;60,&nbsp;but&nbsp;equal3(8) + 4(9) = 24 + 36 = 60 \\quad \\text{\u2192 Not greater than 60, but equal}<\/p>\n\n\n\n<p>But the problem says <strong>&#8220;more than 60&#8221;<\/strong>, not just 60. So this seems false at first glance. However, note: <strong>this is the boundary line (3x + 4y = 60)<\/strong>. Since the problem says the boundary is <strong>shown<\/strong>, and we are to identify a point <strong>above<\/strong> it (which satisfies 3x+4y&gt;603x + 4y &gt; 60), we need to test slightly beyond.<\/p>\n\n\n\n<p>Let\u2019s test <strong>Option A more carefully<\/strong>:<\/p>\n\n\n\n<p>Try 8 math and <strong>9<\/strong> science again: 3(8)+4(9)=24+36=60\u21d2exactly&nbsp;on&nbsp;the&nbsp;boundary&nbsp;line3(8) + 4(9) = 24 + 36 = 60 \\Rightarrow \\text{exactly on the boundary line}<\/p>\n\n\n\n<p>So <strong>this one is NOT valid<\/strong> because it&#8217;s <strong>not greater than 60<\/strong>, only equal.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Option B:<\/strong> 4 math, 6 science 3(4)+4(6)=12+24=36\u2192&nbsp;Too&nbsp;small3(4) + 4(6) = 12 + 24 = 36 \\quad \\text{\u2192 Too small}<\/p>\n\n\n\n<p><strong>Reject<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Option C:<\/strong> 20 math, 10 science 3(20)+4(10)=60+40=100\u2192&nbsp;Greater&nbsp;than&nbsp;603(20) + 4(10) = 60 + 40 = 100 \\quad \\text{\u2192 Greater than 60}<\/p>\n\n\n\n<p><strong>Valid. Keep for now<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Option D:<\/strong> 0 math, 15 science 3(0)+4(15)=0+60=60\u2192&nbsp;Equal&nbsp;only,&nbsp;not&nbsp;&gt;&nbsp;603(0) + 4(15) = 0 + 60 = 60 \\quad \\text{\u2192 Equal only, not &gt; 60}<\/p>\n\n\n\n<p><strong>Reject<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>So now compare the <strong>valid<\/strong> ones:<br>Only <strong>Option C<\/strong> (20 math, 10 science) is fully correct and satisfies the inequality.<\/p>\n\n\n\n<p>\ud83d\udfe9 <strong>Final Correct Answer:<\/strong> <strong>Alexia completed 20 math problems and 10 science problems.<\/strong><\/p>\n\n\n\n<p>This is the only choice that results in <strong>more than 60 minutes<\/strong> of homework time.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\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-banner7-37.jpeg\" alt=\"\" class=\"wp-image-223286\"\/><\/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 > 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-223285","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223285","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=223285"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223285\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}