{"id":169096,"date":"2024-11-19T05:07:01","date_gmt":"2024-11-19T05:07:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=169096"},"modified":"2024-11-19T05:07:03","modified_gmt":"2024-11-19T05:07:03","slug":"the-product-of-two-integers-is-112","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/the-product-of-two-integers-is-112\/","title":{"rendered":"The product of two integers is 112"},"content":{"rendered":"\n

The product of two integers is 112 . One number is four more then three times the other .
Which of the following equations could be used to find one of the numbers ?
A. 3x^2+4x=112
B. 4x^2+3=112
C. 4x^2+3x=112
D. 3x^2+4=112<\/p>\n\n\n\n

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

Let’s break down the problem:<\/p>\n\n\n\n

We are given two key pieces of information:<\/p>\n\n\n\n

    \n
  1. The product of two integers is 112.<\/li>\n\n\n\n
  2. One of the integers is four more than three times the other.<\/li>\n<\/ol>\n\n\n\n

    Let the two integers be (x) and (y). According to the problem:<\/p>\n\n\n\n

      \n
    • (y = 3x + 4) (one number is four more than three times the other),<\/li>\n\n\n\n
    • The product of (x) and (y) is 112, so (x \\cdot y = 112).<\/li>\n<\/ul>\n\n\n\n

      Now, substitute (y = 3x + 4) into the equation for the product of the two numbers:<\/p>\n\n\n\n

      [
      x \\cdot (3x + 4) = 112
      ]<\/p>\n\n\n\n

      Expanding the left side:<\/p>\n\n\n\n

      [
      x(3x) + x(4) = 112
      ]<\/p>\n\n\n\n

      [
      3x^2 + 4x = 112
      ]<\/p>\n\n\n\n

      This is a quadratic equation, which matches option A<\/strong>:<\/p>\n\n\n\n

      [
      3x^2 + 4x = 112
      ]<\/p>\n\n\n\n

      Explanation:<\/h3>\n\n\n\n
        \n
      • We were given that the product of the two numbers equals 112 and that one number is four more than three times the other. This led us to set up a relationship between (x) and (y).<\/li>\n\n\n\n
      • By substituting this relationship (y = 3x + 4) into the equation for their product, we derived a quadratic equation in terms of (x).<\/li>\n\n\n\n
      • The correct equation that could be used to find one of the numbers is (3x^2 + 4x = 112), which corresponds to option A<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        Verifying the other options:<\/h3>\n\n\n\n
          \n
        • Option B: (4x^2 + 3 = 112)<\/strong> \u2014 This does not match the problem, as there is no (3x) term and the numbers involved do not fit the scenario.<\/li>\n\n\n\n
        • Option C: (4x^2 + 3x = 112)<\/strong> \u2014 This equation does not fit the structure derived from the problem.<\/li>\n\n\n\n
        • Option D: (3x^2 + 4 = 112)<\/strong> \u2014 This is also incorrect because it lacks the (x) term needed to represent the relationship between the two integers.<\/li>\n<\/ul>\n\n\n\n

          Thus, the correct answer is A<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

          The product of two integers is 112 . One number is four more then three times the other .Which of the following equations could be used to find one of the numbers ?A. 3x^2+4x=112B. 4x^2+3=112C. 4x^2+3x=112D. 3x^2+4=112 The Correct Answer and Explanation is : Let’s break down the problem: We are given two key pieces […]<\/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-169096","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169096","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=169096"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169096\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=169096"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=169096"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=169096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}