{"id":225216,"date":"2025-06-04T05:21:44","date_gmt":"2025-06-04T05:21:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225216"},"modified":"2025-06-04T05:21:46","modified_gmt":"2025-06-04T05:21:46","slug":"a-store-manager-combines-trail-mix-that-is-30-raisins-with-a-trail-mix-that-is-55-raisins","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/a-store-manager-combines-trail-mix-that-is-30-raisins-with-a-trail-mix-that-is-55-raisins\/","title":{"rendered":"A store manager combines trail mix that is 30% raisins with a trail mix that is 55% raisins."},"content":{"rendered":"\n

A store manager combines trail mix that is 30% raisins with a trail mix that is 55% raisins. He makes 800lb of trail mix that is 40% raisins. How many pounds of each trail mix does the manager use? 2. a confectioner mixes forty liters of 60% sugar syrup with a 10% sugar syrup to make a 20% sugar syrup. how much of the 10% syrup should she use<\/p>\n\n\n\n

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

1. Trail Mix Problem<\/strong><\/h3>\n\n\n\n

We are mixing two trail mixes:<\/p>\n\n\n\n

    \n
  • Mix A: 30% raisins<\/li>\n\n\n\n
  • Mix B: 55% raisins<\/li>\n<\/ul>\n\n\n\n

    We want to make 800 lbs<\/strong> of a new mix that is 40% raisins<\/strong>.<\/p>\n\n\n\n

    Let:<\/p>\n\n\n\n

      \n
    • x<\/strong> = amount (in lbs) of the 30% raisins mix<\/li>\n\n\n\n
    • 800 – x<\/strong> = amount of the 55% raisins mix<\/li>\n<\/ul>\n\n\n\n

      Set up the equation for the total raisins: 0.30x+0.55(800\u2212x)=0.40\u00d78000.30x + 0.55(800 – x) = 0.40 \\times 800<\/p>\n\n\n\n

      Simplify: 0.30x+440\u22120.55x=3200.30x + 440 – 0.55x = 320 \u22120.25x+440=320-0.25x + 440 = 320 \u22120.25x=320\u2212440=\u2212120-0.25x = 320 – 440 = -120 x=\u2212120\u22120.25=480x = \\frac{-120}{-0.25} = 480<\/p>\n\n\n\n

      So:<\/p>\n\n\n\n

        \n
      • 480 lbs of the 30% mix<\/li>\n\n\n\n
      • 800 – 480 = 320 lbs<\/strong> of the 55% mix<\/li>\n<\/ul>\n\n\n\n

        \u2705 Answer<\/strong>: 480 lbs of the 30% mix, 320 lbs of the 55% mix<\/p>\n\n\n\n

        \n\n\n\n

        2. Sugar Syrup Problem<\/strong><\/h3>\n\n\n\n

        We are mixing:<\/p>\n\n\n\n

          \n
        • 40 liters<\/strong> of 60%<\/strong> sugar syrup<\/li>\n\n\n\n
        • An unknown amount x<\/strong> liters of 10%<\/strong> sugar syrup<\/li>\n\n\n\n
        • To create a mix that is 20%<\/strong> sugar syrup<\/li>\n<\/ul>\n\n\n\n

          The total mixture is: (40+x) liters(40 + x) \\text{ liters}<\/p>\n\n\n\n

          The total sugar from each syrup: 0.60\u00d740+0.10x=0.20(40+x)0.60 \\times 40 + 0.10x = 0.20(40 + x)<\/p>\n\n\n\n

          Simplify: 24+0.10x=8+0.20×24 + 0.10x = 8 + 0.20x<\/p>\n\n\n\n

          Subtract 8 from both sides: 16+0.10x=0.20×16 + 0.10x = 0.20x<\/p>\n\n\n\n

          Subtract 0.10x from both sides: 16=0.10×16 = 0.10x x=160.10=160x = \\frac{16}{0.10} = 160<\/p>\n\n\n\n

          \u2705 Answer<\/strong>: 160 liters<\/strong> of the 10% sugar syrup<\/p>\n\n\n\n

          \n\n\n\n

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

          These two problems are examples of mixture problems<\/strong>, a common type in algebra where different concentrations of substances are combined to achieve a desired mixture.<\/p>\n\n\n\n

          In the first problem, we are mixing two types of trail mix with different percentages of raisins. The key is to focus on the total amount of raisins<\/strong>, not just the total weight. We assign a variable (x) to represent the amount of one mix, then express the other amount as a total minus x. By multiplying each amount by its respective raisin percentage, we form an equation that equates the total raisins in the mix to the desired percentage of the total weight. Solving this gives us how much of each type to use.<\/p>\n\n\n\n

          In the second problem, we apply the same principle with sugar syrup. We know how much of the stronger (60%) syrup we have, and we are figuring out how much of the weaker (10%) syrup to add to create a diluted (20%) mixture. Again, we set up an equation based on the total sugar content<\/strong>, solve for x, and determine the amount needed.<\/p>\n\n\n\n

          In both cases, we use the idea that:<\/p>\n\n\n\n

          \n

          (concentration \u00d7 amount) + (concentration \u00d7 amount) = (desired concentration \u00d7 total mixture)<\/p>\n<\/blockquote>\n\n\n\n

          By translating the word problems into algebraic equations and solving step-by-step, we can accurately determine how much of each component to use in the final mixture.<\/p>\n\n\n\n

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

          A store manager combines trail mix that is 30% raisins with a trail mix that is 55% raisins. He makes 800lb of trail mix that is 40% raisins. How many pounds of each trail mix does the manager use? 2. a confectioner mixes forty liters of 60% sugar syrup with a 10% sugar syrup to […]<\/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-225216","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225216","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=225216"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225216\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}