{"id":230221,"date":"2025-06-09T05:28:54","date_gmt":"2025-06-09T05:28:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230221"},"modified":"2025-06-09T05:28:56","modified_gmt":"2025-06-09T05:28:56","slug":"a-distributor-wants-to-make-1000-pounds-of-trail-mix-that-is-8-raisins","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/09\/a-distributor-wants-to-make-1000-pounds-of-trail-mix-that-is-8-raisins\/","title":{"rendered":"A distributor wants to make 1000 pounds of trail mix that is 8% raisins"},"content":{"rendered":"\n<p>A distributor wants to make 1000 pounds of trail mix that is 8% raisins. He will use a mix that is 5% raisins and a mix that is 20% raisins. How many pounds of each should he 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 solve the problem, we can use a system of equations. Let\u2019s define the variables:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let <strong>x<\/strong> = pounds of the 5% raisin mix<\/li>\n\n\n\n<li>Let <strong>y<\/strong> = pounds of the 20% raisin mix<\/li>\n<\/ul>\n\n\n\n<p>We know two things:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The total weight must be 1000 pounds: x+y=1000(Equation\u00a01)x + y = 1000 \\quad \\text{(Equation 1)}x+y=1000(Equation\u00a01)<\/li>\n\n\n\n<li>The final mix should be 8% raisins. The 5% mix contributes 0.05x pounds of raisins, and the 20% mix contributes 0.20y pounds. The total amount of raisins should be 8% of 1000 pounds, or 80 pounds: 0.05x+0.20y=80(Equation\u00a02)0.05x + 0.20y = 80 \\quad \\text{(Equation 2)}0.05x+0.20y=80(Equation\u00a02)<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Solving the system:<\/h3>\n\n\n\n<p>From Equation 1:y=1000\u2212xy = 1000 &#8211; xy=1000\u2212x<\/p>\n\n\n\n<p>Substitute into Equation 2:0.05x+0.20(1000\u2212x)=800.05x + 0.20(1000 &#8211; x) = 800.05x+0.20(1000\u2212x)=800.05x+200\u22120.20x=800.05x + 200 &#8211; 0.20x = 800.05x+200\u22120.20x=80\u22120.15x+200=80-0.15x + 200 = 80\u22120.15x+200=80\u22120.15x=80\u2212200=\u2212120-0.15x = 80 &#8211; 200 = -120\u22120.15x=80\u2212200=\u2212120x=\u2212120\u22120.15=800x = \\frac{-120}{-0.15} = 800x=\u22120.15\u2212120\u200b=800<\/p>\n\n\n\n<p>Now find y:y=1000\u2212x=1000\u2212800=200y = 1000 &#8211; x = 1000 &#8211; 800 = 200y=1000\u2212x=1000\u2212800=200<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>800 pounds<\/strong> of the 5% raisin mix<\/li>\n\n\n\n<li><strong>200 pounds<\/strong> of the 20% raisin mix<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>This type of problem is a classic mixture problem that can be solved using algebra. The distributor needs 1000 pounds of a trail mix that contains 8% raisins. He has two types of mixes available: one with 5% raisins and another with 20% raisins. The goal is to determine how much of each mix he should combine to get exactly 1000 pounds of an 8% raisin mix.<\/p>\n\n\n\n<p>We start by assigning variables: let x be the amount of the 5% mix, and y be the amount of the 20% mix. Since the total amount must be 1000 pounds, we write the first equation:<br><strong>x + y = 1000.<\/strong><\/p>\n\n\n\n<p>Next, we consider the percentage of raisins in each mix. The 5% mix contributes 0.05x pounds of raisins, and the 20% mix contributes 0.20y pounds. Since we want the final 1000-pound mix to be 8% raisins, we want a total of 80 pounds of raisins (because 8% of 1000 is 80). This gives us the second equation:<br><strong>0.05x + 0.20y = 80.<\/strong><\/p>\n\n\n\n<p>By substituting one equation into the other, we eliminate a variable and solve for x. After finding x, we substitute back to find y. The solution gives us 800 pounds of the 5% mix and 200 pounds of the 20% mix. When combined, these produce a 1000-pound mix with exactly 8% raisins, satisfying both conditions of the problem.<\/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-banner9-205.jpeg\" alt=\"\" class=\"wp-image-230222\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A distributor wants to make 1000 pounds of trail mix that is 8% raisins. He will use a mix that is 5% raisins and a mix that is 20% raisins. How many pounds of each should he use? The Correct Answer and Explanation is: To solve the problem, we can use a system of equations. [&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-230221","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230221","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=230221"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230221\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230221"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230221"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}