{"id":279500,"date":"2025-08-04T06:10:30","date_gmt":"2025-08-04T06:10:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=279500"},"modified":"2025-08-04T06:10:32","modified_gmt":"2025-08-04T06:10:32","slug":"penelope-went-to-the-store-to-buy-x-pounds-she-spent-less-than-10","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/04\/penelope-went-to-the-store-to-buy-x-pounds-she-spent-less-than-10\/","title":{"rendered":"Penelope went to the store to buy x pounds she spent less than $10."},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-309.png\" alt=\"\" class=\"wp-image-279501\"\/><\/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 reasonable solutions are (0, 2), (3, 2.5), and (1.5, 3).<\/p>\n\n\n\n<p>To determine the reasonable solutions, we must check two conditions for each ordered pair (x, y). First, since x and y represent pounds of items being purchased, neither value can be negative. This is the &#8220;reasonable&#8221; part of the question. Second, the pair must satisfy the inequality 1.10x + 2.50y &lt; 10, meaning the total cost is less than $10.<\/p>\n\n\n\n<p>Let&#8217;s test each option:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(-1, 4):<\/strong>\u00a0This is not a reasonable solution. Although it mathematically satisfies the inequality (1.10(-1) + 2.50(4) = 8.90, which is less than 10), one cannot buy a negative amount of an item.<\/li>\n\n\n\n<li><strong>(0, 2):<\/strong>\u00a0This is a reasonable solution. Both values are non-negative. The cost is 1.10(0) + 2.50(2) = 0 + 5.00 = $5.00. Since $5.00 is less than $10, this option is correct.<\/li>\n\n\n\n<li><strong>(3, 2.5):<\/strong>\u00a0This is a reasonable solution. Both values are positive. The cost is 1.10(3) + 2.50(2.5) = 3.30 + 6.25 = $9.55. Since $9.55 is less than $10, this option is correct.<\/li>\n\n\n\n<li><strong>(2, 4):<\/strong>\u00a0This is not a solution. The cost is 1.10(2) + 2.50(4) = 2.20 + 10.00 = $12.20. This amount is not less than $10, so it violates the inequality.<\/li>\n\n\n\n<li><strong>(0.5, 3.78):<\/strong>\u00a0This is not a solution. The cost is 1.10(0.5) + 2.50(3.78) = 0.55 + 9.45 = $10.00. The inequality requires the total to be strictly less than $10, and $10.00 is equal to, not less than, $10.<\/li>\n\n\n\n<li><strong>(1.5, 3):<\/strong>\u00a0This is a reasonable solution. Both values are positive. The cost is 1.10(1.5) + 2.50(3) = 1.65 + 7.50 = $9.15. Since $9.15 is less than $10, this option is correct.<\/li>\n<\/ul>\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-banner4-68.jpeg\" alt=\"\" class=\"wp-image-279502\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct reasonable solutions are (0, 2), (3, 2.5), and (1.5, 3). To determine the reasonable solutions, we must check two conditions for each ordered pair (x, y). First, since x and y represent pounds of items being purchased, neither value can be negative. This is the &#8220;reasonable&#8221; part [&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-279500","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279500","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=279500"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279500\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=279500"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=279500"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=279500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}