{"id":233257,"date":"2025-06-12T21:11:04","date_gmt":"2025-06-12T21:11:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233257"},"modified":"2025-06-12T21:11:06","modified_gmt":"2025-06-12T21:11:06","slug":"pat-invested-a-total-of256-how-much-did-pat-invest-at-10-percent-and-how-much-at-8-percent","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/pat-invested-a-total-of256-how-much-did-pat-invest-at-10-percent-and-how-much-at-8-percent\/","title":{"rendered":"Pat invested a total of256, how much did Pat invest at 10 percent and how much at 8 percent"},"content":{"rendered":"\n

Pat invested a total of
256, how much did Pat invest at 10 percent and how much at 8 percent?<\/p>\n\n\n\n

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

Answer:<\/strong><\/p>\n\n\n\n

Let the amount Pat invested at 10%<\/strong> be x<\/strong> dollars.
Then, the amount invested at 8%<\/strong> is (256 – x)<\/strong> dollars.<\/p>\n\n\n\n

Assume the interest earned from both investments is the same.<\/p>\n\n\n\n

Then:<\/p>\n\n\n\n

\n

Interest from 10% investment = Interest from 8% investment
0.10x=0.08(256\u2212x)0.10x = 0.08(256 – x)0.10x=0.08(256\u2212x)<\/p>\n<\/blockquote>\n\n\n\n

Solve the equation:<\/strong>0.10x=0.08(256\u2212x)0.10x = 0.08(256 – x)0.10x=0.08(256\u2212x)0.10x=20.48\u22120.08×0.10x = 20.48 – 0.08×0.10x=20.48\u22120.08×0.10x+0.08x=20.480.10x + 0.08x = 20.480.10x+0.08x=20.480.18x=20.480.18x = 20.480.18x=20.48x=20.480.18=113.78 (rounded to two decimal places)x = \\frac{20.48}{0.18} = 113.78 \\ (\\text{rounded to two decimal places})x=0.1820.48\u200b=113.78 (rounded to two decimal places)<\/p>\n\n\n\n

Therefore:<\/p>\n\n\n\n

    \n
  • Pat invested $113.78 at 10%<\/strong><\/li>\n\n\n\n
  • Pat invested $142.22 at 8%<\/strong> (since 256 \u2212 113.78 = 142.22)<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Explanation<\/strong><\/p>\n\n\n\n

    To solve a problem involving two parts of an investment at different interest rates, the key is to set up a variable to represent one part of the investment and express the other part in terms of that same variable. In this case, the total amount Pat invested is $256. Suppose the amount invested at 10% interest is x<\/em> dollars. Then the remaining amount, which is (256 \u2013 x)<\/em> dollars, must have been invested at 8% interest.<\/p>\n\n\n\n

    The problem assumes that the interest earned from both investments is equal. To express this, we use the formula for simple interest:
    Interest = Principal \u00d7 Rate.<\/strong><\/p>\n\n\n\n

    The interest from the 10% investment is 0.10 \u00d7 x<\/strong>, and the interest from the 8% investment is 0.08 \u00d7 (256 \u2212 x)<\/strong>. Setting these equal gives a linear equation, which can be solved by isolating the variable. After solving, it turns out Pat invested $113.78 at 10% and the rest, $142.22, at 8%.<\/p>\n\n\n\n

    This method of breaking a total into parts using a variable, then setting up an equation based on equal outcomes (like equal interest), is a common strategy in algebra. It allows for a logical way to handle mixture and investment problems and to find how much money was allocated to each interest rate, even when the total and conditions are all that\u2019s known.<\/p>\n\n\n\n

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

    Pat invested a total of256, how much did Pat invest at 10 percent and how much at 8 percent? The Correct Answer and Explanation is: Answer: Let the amount Pat invested at 10% be x dollars.Then, the amount invested at 8% is (256 – x) dollars. Assume the interest earned from both investments is the […]<\/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-233257","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233257","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=233257"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233257\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233257"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233257"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233257"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}