{"id":238114,"date":"2025-06-17T20:31:19","date_gmt":"2025-06-17T20:31:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238114"},"modified":"2025-06-17T20:31:22","modified_gmt":"2025-06-17T20:31:22","slug":"scott-uses-45-cent-stamps-and-8-cent-stamps-to-mail-a-gift-card-to-a-friend","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/scott-uses-45-cent-stamps-and-8-cent-stamps-to-mail-a-gift-card-to-a-friend\/","title":{"rendered":"Scott uses 45 -cent stamps and 8 -cent stamps to mail a gift card to a friend"},"content":{"rendered":"\n<p>Scott uses 45 -cent stamps and 8 -cent stamps to mail a gift card to a friend. If the postage is $2.07 , how many of each stamp did Scott use?<\/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>To find how many 45-cent stamps and 8-cent stamps Scott used to make $2.07 in postage, we first convert the total cost into cents:2.07&nbsp;dollars=207&nbsp;cents2.07 \\text{ dollars} = 207 \\text{ cents}2.07&nbsp;dollars=207&nbsp;cents<\/p>\n\n\n\n<p>Let:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>xxx = number of 45-cent stamps<\/li>\n\n\n\n<li>yyy = number of 8-cent stamps<\/li>\n<\/ul>\n\n\n\n<p>The total postage equation becomes:45x+8y=20745x + 8y = 20745x+8y=207<\/p>\n\n\n\n<p>This is a linear Diophantine equation, which means we are looking for integer solutions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Trial and Error to Find Integer Solution<\/h3>\n\n\n\n<p>Let\u2019s test different values of xxx to find one where yyy is also a whole number.<\/p>\n\n\n\n<p>Try x=3x = 3x=3:45(3)+8y=207\u21d2135+8y=207\u21d28y=72\u21d2y=945(3) + 8y = 207 \\Rightarrow 135 + 8y = 207 \\Rightarrow 8y = 72 \\Rightarrow y = 945(3)+8y=207\u21d2135+8y=207\u21d28y=72\u21d2y=9<\/p>\n\n\n\n<p>That works! So one solution is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3 of the 45-cent stamps<\/li>\n\n\n\n<li>9 of the 8-cent stamps<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s double-check:3(45)+9(8)=135+72=2073(45) + 9(8) = 135 + 72 = 2073(45)+9(8)=135+72=207<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>Scott used <strong>3 of the 45-cent stamps<\/strong> and <strong>9 of the 8-cent stamps<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p>This problem involves solving a linear equation with two unknowns. The total postage required is $2.07. To make the math simpler, we convert dollars into cents, because the stamps are priced in cents. Thus, $2.07 becomes 207 cents.<\/p>\n\n\n\n<p>We assign variables to represent how many stamps of each kind Scott used: let xxx be the number of 45-cent stamps, and yyy the number of 8-cent stamps. The total value of the stamps must equal 207 cents, which gives the equation 45x+8y=20745x + 8y = 20745x+8y=207.<\/p>\n\n\n\n<p>Since we are working with whole items (stamps), the solution must be integers. We use substitution or trial-and-error to test small values of xxx and solve for yyy. We are looking for values that make both xxx and yyy integers.<\/p>\n\n\n\n<p>Trying x=3x = 3x=3, we solve for yyy and find it equals 9. This means Scott used 3 stamps worth 45 cents and 9 stamps worth 8 cents.<\/p>\n\n\n\n<p>We can verify this by calculating the total postage: 3\u00d745=1353 \\times 45 = 1353\u00d745=135 cents and 9\u00d78=729 \\times 8 = 729\u00d78=72 cents. Their sum is 135+72=207135 + 72 = 207135+72=207 cents, which is correct.<\/p>\n\n\n\n<p>This method is useful for solving problems where combinations of fixed amounts must total a specific value. These types of problems appear in real-life budgeting, postage, and inventory scenarios.<\/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-banner8-989.jpeg\" alt=\"\" class=\"wp-image-238115\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Scott uses 45 -cent stamps and 8 -cent stamps to mail a gift card to a friend. If the postage is $2.07 , how many of each stamp did Scott use? The Correct Answer and Explanation is: To find how many 45-cent stamps and 8-cent stamps Scott used to make $2.07 in postage, we first [&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-238114","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238114","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=238114"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238114\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}