Orly uses 2 cups of raisins for every 9 cups of trail mix she makes. How many cups of trail mix will she make if she uses 12 cups of raisins? 2(2)\/(3) cups 54 cups 9 cups 1(1)\/(2) cups<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the problem, we use the ratio Orly follows: 2 cups of raisins for every 9 cups of trail mix<\/strong>. This can be written as: 2\u2009cups of raisins9\u2009cups of trail mix\\frac{2 \\, \\text{cups of raisins}}{9 \\, \\text{cups of trail mix}}<\/p>\n\n\n\n We need to determine how many cups of trail mix she can make if she uses 12 cups of raisins<\/strong>. To do this, set up a proportion: 29=12x\\frac{2}{9} = \\frac{12}{x}<\/p>\n\n\n\n Here, xx represents the number of cups of trail mix. Solve for xx by cross-multiplying: 2\u22c5x=12\u22c592 \\cdot x = 12 \\cdot 9 2x=1082x = 108 x=1082=54x = \\frac{108}{2} = 54<\/p>\n\n\n\n Thus, Orly can make 54 cups of trail mix<\/strong> if she uses 12 cups of raisins.<\/p>\n\n\n\n The relationship between the ingredients is proportional, meaning the ratio of raisins to trail mix remains constant no matter how much she makes. If 2 cups of raisins are needed for every 9 cups of trail mix, then multiplying both amounts by the same factor will maintain this ratio.<\/p>\n\n\n\n In this case, 12 cups of raisins is 6 times<\/strong> the amount of raisins in the original ratio (since 12\u00f72=612 \\div 2 = 6). Therefore, the amount of trail mix must also increase by a factor of 6. Since 9 cups of trail mix are made with 2 cups of raisins, multiplying 9 by 6 gives: 9\u22c56=54\u2009cups of trail mix.9 \\cdot 6 = 54 \\, \\text{cups of trail mix}.<\/p>\n\n\n\n By solving proportionally, we ensure the quantities scale correctly. The answer is 54 cups of trail mix<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Orly uses 2 cups of raisins for every 9 cups of trail mix she makes. How many cups of trail mix will she make if she uses 12 cups of raisins? 2(2)\/(3) cups 54 cups 9 cups 1(1)\/(2) cups The correct answer and explanation is: To solve the problem, we use the ratio Orly follows: […]<\/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-185934","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185934","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=185934"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185934\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185934"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185934"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185934"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n