{"id":225778,"date":"2025-06-04T15:17:55","date_gmt":"2025-06-04T15:17:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225778"},"modified":"2025-06-04T15:17:57","modified_gmt":"2025-06-04T15:17:57","slug":"gallons-eli-wants-to-combine-0-5-gallon-of-a-10-acid-solution-acid-amount-of-with-some-35-acid-solution-to-make-a-15-acid-of-concentra-solution","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/gallons-eli-wants-to-combine-0-5-gallon-of-a-10-acid-solution-acid-amount-of-with-some-35-acid-solution-to-make-a-15-acid-of-concentra-solution\/","title":{"rendered":"Gallons Eli wants to combine 0.5 gallon of a 10\\% acid solution Acid Amount of with some 35\\% acid solution to make a 15\\% acid of Concentra- solution."},"content":{"rendered":"\n

Gallons Eli wants to combine 0.5 gallon of a 10\\% acid solution Acid Amount of with some 35\\% acid solution to make a 15\\% acid of Concentra- solution. Acid Solution tion How much of the 35\\% acid solution should Eli add? 10\\% 0.5 0.10 gallon Acid (0.10)(0.5) 35\\%
0.35 Acid 0.35
Mixture
0.15 0.15(
+0.5) (0.10)(0.5)+0.35
= 0.15(
+0.5)<\/p>\n\n\n\n

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

To solve this problem, we will use the method of solving by setting up an equation based on the total amount of acid in the mixture<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Problem Restatement<\/strong><\/h3>\n\n\n\n

Eli has:<\/p>\n\n\n\n

    \n
  • 0.5 gallon<\/strong> of a 10% acid solution<\/strong>, and<\/li>\n\n\n\n
  • Wants to add x gallons<\/strong> of a 35% acid solution<\/strong><\/li>\n\n\n\n
  • The result should be a 15% acid solution<\/strong><\/li>\n<\/ul>\n\n\n\n

    We are to find the amount of 35% acid solution (x gallons)<\/strong> to add.<\/p>\n\n\n\n

    \n\n\n\n

    Step-by-Step Solution<\/strong><\/h3>\n\n\n\n

    Let xx be the number of gallons of 35% acid solution that Eli needs to add.<\/p>\n\n\n\n

    We calculate the total acid content before and after mixing:<\/p>\n\n\n\n

      \n
    1. Acid in 10% solution:<\/strong> 0.10\u00d70.5=0.05\u00a0gallons\u00a0of\u00a0pure\u00a0acid0.10 \\times 0.5 = 0.05 \\text{ gallons of pure acid}<\/li>\n\n\n\n
    2. Acid in x gallons of 35% solution:<\/strong> 0.35\u00d7x=0.35x\u00a0gallons\u00a0of\u00a0pure\u00a0acid0.35 \\times x = 0.35x \\text{ gallons of pure acid}<\/li>\n\n\n\n
    3. Total volume of the new mixture:<\/strong> 0.5+x\u00a0gallons0.5 + x \\text{ gallons}<\/li>\n\n\n\n
    4. Desired concentration in mixture (15%):<\/strong> 0.15\u00d7(0.5+x)\u00a0gallons\u00a0of\u00a0pure\u00a0acid0.15 \\times (0.5 + x) \\text{ gallons of pure acid}<\/li>\n<\/ol>\n\n\n\n

      Now we set up the equation: 0.05+0.35x=0.15(0.5+x)0.05 + 0.35x = 0.15(0.5 + x)<\/p>\n\n\n\n

      Expand both sides: 0.05+0.35x=0.075+0.15×0.05 + 0.35x = 0.075 + 0.15x<\/p>\n\n\n\n

      Subtract 0.15×0.15x from both sides: 0.05+0.20x=0.0750.05 + 0.20x = 0.075<\/p>\n\n\n\n

      Subtract 0.05 from both sides: 0.20x=0.0250.20x = 0.025<\/p>\n\n\n\n

      Now divide both sides by 0.20: x=0.0250.20=0.125x = \\frac{0.025}{0.20} = 0.125<\/p>\n\n\n\n

      \n\n\n\n

      Final Answer:<\/strong><\/h3>\n\n\n\n

      Eli should add 0.125 gallons (or 1\/8 gallon) of the 35% acid solution.<\/strong><\/p>\n\n\n\n

      \n\n\n\n

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

      This problem is a classic example of mixture problems<\/strong>, where we are combining two solutions of different concentrations to obtain a solution of a desired concentration. The key idea is to track the amount of pure acid<\/strong> in each component and ensure that the total amount of acid in the final mixture matches the desired percentage.<\/p>\n\n\n\n

      Eli starts with 0.5 gallon of 10% acid solution. Since 10% of this is acid, it contains 0.05 gallons of pure acid. He wants to add some amount xx of 35% solution. The pure acid in this part is 0.35×0.35x. The final mixture will have a total volume of 0.5+x0.5 + x gallons, and we want this to be 15% acid. That means the amount of pure acid in the final mixture must be 0.15(0.5+x)0.15(0.5 + x).<\/p>\n\n\n\n

      By setting up the equation 0.05+0.35x=0.15(0.5+x)0.05 + 0.35x = 0.15(0.5 + x), we equate the total amount of acid in the mixture to what it must be to reach 15% concentration. Solving the equation step-by-step allows us to isolate xx, the unknown quantity of 35% acid to add.<\/p>\n\n\n\n

      The result shows that only 0.125 gallons<\/strong>, or 1\/8 of a gallon<\/strong>, of the 35% acid solution is needed to achieve the target concentration. This is a relatively small amount because 35% is much stronger than 15%, so not much of it is needed to shift the concentration upward.<\/p>\n\n\n\n

      This process illustrates how algebra and proportional reasoning are used in real-life applications such as chemistry, pharmacology, and industrial mixing.<\/p>\n\n\n\n

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

      Gallons Eli wants to combine 0.5 gallon of a 10\\% acid solution Acid Amount of with some 35\\% acid solution to make a 15\\% acid of Concentra- solution. Acid Solution tion How much of the 35\\% acid solution should Eli add? 10\\% 0.5 0.10 gallon Acid (0.10)(0.5) 35\\%0.35 Acid 0.35Mixture0.15 0.15(+0.5) (0.10)(0.5)+0.35= 0.15(+0.5) The Correct […]<\/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-225778","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225778","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=225778"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225778\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225778"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225778"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}