{"id":227681,"date":"2025-06-06T11:26:31","date_gmt":"2025-06-06T11:26:31","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227681"},"modified":"2025-06-06T11:26:34","modified_gmt":"2025-06-06T11:26:34","slug":"ben-and-joel-are-raising-money-for-their-class-trip-by-selling-wrapping-paper","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/ben-and-joel-are-raising-money-for-their-class-trip-by-selling-wrapping-paper\/","title":{"rendered":"Ben and Joel are raising money for their class trip by selling wrapping paper."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised<br>51.50 by selling 8 rolls of solid paper and 15 rolls of printed paper. Find the cost of each type of wrapping paper.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><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<h3 class=\"wp-block-heading\">Step 1: Set up variables<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>xxx = cost of one roll of solid wrapping paper (in dollars)<\/li>\n\n\n\n<li>yyy = cost of one roll of printed wrapping paper (in dollars)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We are told Ben sold:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>8 rolls of solid paper \u2192 worth 8x8x8x<\/li>\n\n\n\n<li>15 rolls of printed paper \u2192 worth 15y15y15y<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Altogether, Ben raised $51.50. So we set up the equation:8x+15y=51.50(1)8x + 15y = 51.50 \\tag{1}8x+15y=51.50(1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, we need more information to solve for <strong>both<\/strong> xxx and yyy, such as a second equation involving Joel\u2019s sales. But the problem does not mention Joel&#8217;s sales or a second equation. So, with only one equation and two variables, we cannot find a unique solution unless one of the costs is known.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Let&#8217;s assume that Joel raised <strong>the same total amount<\/strong> or used the same pricing. Suppose Joel sold a different combination and raised a certain amount \u2014 but since we are not given Joel\u2019s data, we cannot do that. So instead, maybe the problem is <strong>missing information<\/strong>, or <strong>we&#8217;re supposed to assume<\/strong> the prices are whole or common decimal values.<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s try possible values:<br>Assume:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Solid paper: $2.00 \u2192 x=2.00x = 2.00x=2.00<\/li>\n\n\n\n<li>Printed paper: $2.50 \u2192 y=2.50y = 2.50y=2.50<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Check:8(2.00)+15(2.50)=16+37.50=53.50\u226051.508(2.00) + 15(2.50) = 16 + 37.50 = 53.50 \\ne 51.508(2.00)+15(2.50)=16+37.50=53.50\ue020=51.50<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Try:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x=1.50x = 1.50x=1.50, y=2.50y = 2.50y=2.50<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">8(1.50)+15(2.50)=12+37.50=49.50\u226051.508(1.50) + 15(2.50) = 12 + 37.50 = 49.50 \\ne 51.508(1.50)+15(2.50)=12+37.50=49.50\ue020=51.50<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Try:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x=2.00x = 2.00x=2.00, y=2.35y = 2.35y=2.35<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">8(2.00)+15(2.35)=16+35.25=51.258(2.00) + 15(2.35) = 16 + 35.25 = 51.258(2.00)+15(2.35)=16+35.25=51.25<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Try:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x=2.00x = 2.00x=2.00, y=2.37y = 2.37y=2.37<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">8(2.00)+15(2.37)=16+35.55=51.558(2.00) + 15(2.37) = 16 + 35.55 = 51.558(2.00)+15(2.37)=16+35.55=51.55<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Eventually, try:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x=2.00x = 2.00x=2.00, y=2.35y = 2.35y=2.35<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">8x+15y=16+35.25=51.258x + 15y = 16 + 35.25 = 51.258x+15y=16+35.25=51.25<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">No simple values give us <strong>exactly<\/strong> 51.50.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Best approach: Solve algebraically<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s assume Joel raised a different amount to give us a second equation. But we don&#8217;t have this. Thus:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udc49 <strong>There is not enough information to find a unique solution<\/strong> unless:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The price of one of the papers is known, or<\/li>\n\n\n\n<li>We are given Joel\u2019s sales to form a second equation.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>We cannot determine the cost of each type of wrapping paper with the given information alone.<\/strong> Only one equation with two unknowns was provided.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If additional info is given \u2014 such as Joel&#8217;s total sales or price of one type \u2014 then we could solve the system.<\/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-banner8-94.jpeg\" alt=\"\" class=\"wp-image-227682\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised51.50 by selling 8 rolls of solid paper and 15 rolls of printed paper. Find the cost of each type of wrapping paper. The Correct Answer and Explanation is: Step 1: Set up variables Let: We are told Ben sold: [&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-227681","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227681","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=227681"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227681\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227681"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227681"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227681"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}