{"id":229929,"date":"2025-06-08T16:21:43","date_gmt":"2025-06-08T16:21:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229929"},"modified":"2025-06-08T16:21:45","modified_gmt":"2025-06-08T16:21:45","slug":"alex-and-freddy-collect-stamps","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/alex-and-freddy-collect-stamps\/","title":{"rendered":"Alex and Freddy collect stamps."},"content":{"rendered":"\n

Alex and Freddy collect stamps. The number of stamps in Alex’s collection is in a ratio of 3:5 to the number of stamps in Freddy’s collection. If Freddy gives Alex 10 stamps, the ratio will change to 7:9. How many stamps are in both collections together?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let the number of stamps Alex has be 3x<\/strong>, and the number of stamps Freddy has be 5x<\/strong>, since their collections are in the ratio 3:5.<\/p>\n\n\n\n

Step 1: After the exchange<\/h3>\n\n\n\n

Freddy gives Alex 10 stamps.<\/p>\n\n\n\n

    \n
  • Alex\u2019s new amount = 3x + 10<\/li>\n\n\n\n
  • Freddy\u2019s new amount = 5x \u2212 10<\/li>\n<\/ul>\n\n\n\n

    Now, their new ratio becomes 7:9<\/strong>.3x+105x\u221210=79\\frac{3x + 10}{5x – 10} = \\frac{7}{9}5x\u2212103x+10\u200b=97\u200b<\/p>\n\n\n\n

    Step 2: Solve the proportion<\/h3>\n\n\n\n

    Cross-multiply:9(3x+10)=7(5x\u221210)9(3x + 10) = 7(5x – 10)9(3x+10)=7(5x\u221210)27x+90=35x\u22127027x + 90 = 35x – 7027x+90=35x\u221270<\/p>\n\n\n\n

    Subtract 27x from both sides:90=8x\u22127090 = 8x – 7090=8x\u221270<\/p>\n\n\n\n

    Add 70 to both sides:160=8×160 = 8×160=8xx=20x = 20x=20<\/p>\n\n\n\n

    Step 3: Calculate number of stamps<\/h3>\n\n\n\n
      \n
    • Alex originally had: 3x=3(20)=603x = 3(20) = 603x=3(20)=60<\/li>\n\n\n\n
    • Freddy originally had: 5x=5(20)=1005x = 5(20) = 1005x=5(20)=100<\/li>\n<\/ul>\n\n\n\n

      Total number of stamps = 60 + 100 = 160<\/strong><\/p>\n\n\n\n

      \n\n\n\n

      Explanation<\/h3>\n\n\n\n

      This problem is a classic example of a ratio and proportion<\/strong> word problem. We are told that Alex and Freddy collect stamps and their stamp counts are in a 3:5 ratio. This means if Alex has 3 parts, Freddy has 5 parts of some common quantity. Representing these quantities algebraically helps us keep track of the changes \u2014 so we let Alex have 3x and Freddy 5x stamps.<\/p>\n\n\n\n

      Next, Freddy gives Alex 10 stamps, altering both their totals. Now Alex has more, and Freddy has fewer. The new ratio is 7:9, which gives us a proportion we can solve. Writing the equation:3x+105x\u221210=79\\frac{3x + 10}{5x – 10} = \\frac{7}{9}5x\u2212103x+10\u200b=97\u200b<\/p>\n\n\n\n

      we use cross multiplication<\/strong>, a standard technique in solving proportions. Multiplying across gives a linear equation, which we simplify to find x=20x = 20x=20.<\/p>\n\n\n\n

      With this value of x, we substitute back to find the actual number of stamps each person originally had: Alex had 60, and Freddy had 100. Adding both gives the total collection: 160 stamps<\/strong>.<\/p>\n\n\n\n

      This problem tests a student\u2019s ability to model a situation with variables, understand how changes affect ratios, and apply algebraic methods to find a solution. It\u2019s a practical example of how proportional reasoning is used to understand real-world exchanges.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Alex and Freddy collect stamps. The number of stamps in Alex’s collection is in a ratio of 3:5 to the number of stamps in Freddy’s collection. If Freddy gives Alex 10 stamps, the ratio will change to 7:9. How many stamps are in both collections together? The Correct Answer and Explanation is: Let the number […]<\/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-229929","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229929","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=229929"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229929\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229929"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229929"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229929"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}