{"id":213544,"date":"2025-05-11T17:15:40","date_gmt":"2025-05-11T17:15:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=213544"},"modified":"2025-05-11T17:15:42","modified_gmt":"2025-05-11T17:15:42","slug":"alan-has-twice-as-many-dimes-as-he-has-quarters-and-10-more-nickels-than-dimes","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/11\/alan-has-twice-as-many-dimes-as-he-has-quarters-and-10-more-nickels-than-dimes\/","title":{"rendered":"Alan has twice as many dimes as he has quarters and 10 more nickels than dimes."},"content":{"rendered":"\n<p>Alan has twice as many dimes as he has quarters and 10 more nickels than dimes. The remaining 35 coins are pennies. How many of quarters, dimes, and nickels does he have if he has $2.50?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we will use algebra to set up and solve a system of equations based on the information provided.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Let:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>qq = number of <strong>quarters<\/strong><\/li>\n\n\n\n<li>dd = number of <strong>dimes<\/strong><\/li>\n\n\n\n<li>nn = number of <strong>nickels<\/strong><\/li>\n\n\n\n<li>pp = number of <strong>pennies<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Given relationships:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Alan has <strong>twice as many dimes as quarters<\/strong>:<br>d=2qd = 2q<\/li>\n\n\n\n<li>Alan has <strong>10 more nickels than dimes<\/strong>:<br>n=d+10n = d + 10<\/li>\n\n\n\n<li>Alan has <strong>35 pennies<\/strong>:<br>p=35p = 35<\/li>\n\n\n\n<li>The <strong>total value<\/strong> of all coins is <strong>$2.50<\/strong> or <strong>250 cents<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p>Now let\u2019s write the value equation using cents:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Quarters are worth 25 cents: 25q25q<\/li>\n\n\n\n<li>Dimes are worth 10 cents: 10d10d<\/li>\n\n\n\n<li>Nickels are worth 5 cents: 5n5n<\/li>\n\n\n\n<li>Pennies are worth 1 cent: 1p=351p = 35<\/li>\n<\/ul>\n\n\n\n<p>So the total value equation is: 25q+10d+5n+35=25025q + 10d + 5n + 35 = 250<\/p>\n\n\n\n<p>Now substitute the expressions for dd and nn:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>d=2qd = 2q<\/li>\n\n\n\n<li>n=d+10=2q+10n = d + 10 = 2q + 10<\/li>\n<\/ul>\n\n\n\n<p>Substitute into the total value equation: 25q+10(2q)+5(2q+10)+35=25025q + 10(2q) + 5(2q + 10) + 35 = 250<\/p>\n\n\n\n<p>Now simplify: 25q+20q+10q+50+35=25025q + 20q + 10q + 50 + 35 = 250<\/p>\n\n\n\n<p>Combine like terms: (25q+20q+10q)+85=250\u21d255q+85=250(25q + 20q + 10q) + 85 = 250 \\Rightarrow 55q + 85 = 250<\/p>\n\n\n\n<p>Subtract 85 from both sides: 55q=16555q = 165<\/p>\n\n\n\n<p>Divide by 55: q=3q = 3<\/p>\n\n\n\n<p>Now solve for the other coins:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>d=2q=2(3)=6d = 2q = 2(3) = 6<\/li>\n\n\n\n<li>n=d+10=6+10=16n = d + 10 = 6 + 10 = 16<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Quarters<\/strong>: 3<\/li>\n\n\n\n<li><strong>Dimes<\/strong>: 6<\/li>\n\n\n\n<li><strong>Nickels<\/strong>: 16<\/li>\n\n\n\n<li><strong>Pennies<\/strong>: 35<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Check Total Value:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Quarters: 3 \u00d7 25 = 75<\/li>\n\n\n\n<li>Dimes: 6 \u00d7 10 = 60<\/li>\n\n\n\n<li>Nickels: 16 \u00d7 5 = 80<\/li>\n\n\n\n<li>Pennies: 35 \u00d7 1 = 35<br><strong>Total<\/strong>: 75 + 60 + 80 + 35 = <strong>250 cents = $2.50<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u2705 <strong>The answer is correct.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alan has twice as many dimes as he has quarters and 10 more nickels than dimes. The remaining 35 coins are pennies. How many of quarters, dimes, and nickels does he have if he has $2.50? The Correct Answer and Explanation is: To solve this problem, we will use algebra to set up and solve [&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-213544","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213544","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=213544"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213544\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=213544"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=213544"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=213544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}