{"id":199194,"date":"2025-03-10T20:13:30","date_gmt":"2025-03-10T20:13:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199194"},"modified":"2025-03-10T20:13:32","modified_gmt":"2025-03-10T20:13:32","slug":"allison-has-5-times-as-many-baseball-cards-as-football-cards","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/10\/allison-has-5-times-as-many-baseball-cards-as-football-cards\/","title":{"rendered":"Allison has 5 times as many baseball cards as football cards"},"content":{"rendered":"\n<p>Allison has 5 times as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball cards does Allison have?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine how many baseball cards Allison has, let&#8217;s define variables and set up an equation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Define Variables<\/h3>\n\n\n\n<p>Let:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( x ) be the number of football cards Allison has.<\/li>\n\n\n\n<li>Since she has <strong>5 times as many baseball cards<\/strong> as football cards, the number of baseball cards she has is ( 5x ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Set Up the Equation<\/h3>\n\n\n\n<p>The problem states that <strong>the total number of baseball and football cards is 120<\/strong>. This gives the equation:<\/p>\n\n\n\n<p>[<br>x + 5x = 120<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solve for ( x )<\/h3>\n\n\n\n<p>[<br>6x = 120<br>]<\/p>\n\n\n\n<p>[<br>x = \\frac{120}{6} = 20<br>]<\/p>\n\n\n\n<p>So, Allison has <strong>20 football cards<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Find the Number of Baseball Cards<\/h3>\n\n\n\n<p>Since she has 5 times as many baseball cards:<\/p>\n\n\n\n<p>[<br>5 \\times 20 = 100<br>]<\/p>\n\n\n\n<p>Thus, <strong>Allison has 100 baseball cards<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Verify the Answer<\/h3>\n\n\n\n<p>Checking the total:<\/p>\n\n\n\n<p>[<br>100 + 20 = 120<br>]<\/p>\n\n\n\n<p>which matches the given total, confirming our answer is correct.<\/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 is an example of an algebraic word problem that requires setting up and solving an equation. We started by defining variables: the number of football cards as ( x ) and the number of baseball cards as ( 5x ). Since the total number of both cards is given as 120, we wrote the equation:<\/p>\n\n\n\n<p>[<br>x + 5x = 120<br>]<\/p>\n\n\n\n<p>This equation expresses that the sum of football and baseball cards must equal 120. By simplifying, we combined like terms:<\/p>\n\n\n\n<p>[<br>6x = 120<br>]<\/p>\n\n\n\n<p>Next, we solved for ( x ) by dividing both sides by 6:<\/p>\n\n\n\n<p>[<br>x = 20<br>]<\/p>\n\n\n\n<p>This means Allison has 20 football cards. Since the number of baseball cards is 5 times that, we computed:<\/p>\n\n\n\n<p>[<br>5 \\times 20 = 100<br>]<\/p>\n\n\n\n<p>Thus, she has <strong>100 baseball cards<\/strong>.<\/p>\n\n\n\n<p>To verify, we checked that ( 100 + 20 = 120 ), confirming that our calculations are correct.<\/p>\n\n\n\n<p>This problem demonstrates how algebra simplifies complex relationships into solvable equations. By translating the word problem into an equation, solving for ( x ), and verifying the solution, we ensured accuracy. This method is widely used in real-world applications, such as finance and engineering, where relationships between quantities must be determined systematically.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Allison has 5 times as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball cards does Allison have? The correct answer and explanation is : To determine how many baseball cards Allison has, let&#8217;s define variables and set up an equation. Step 1: Define Variables Let: [&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-199194","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199194","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=199194"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199194\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199194"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199194"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}