{"id":158835,"date":"2024-10-30T18:09:53","date_gmt":"2024-10-30T18:09:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=158835"},"modified":"2024-10-30T18:09:56","modified_gmt":"2024-10-30T18:09:56","slug":"what-number-multiplies-to-make-196-but-adds-to-make-53","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/30\/what-number-multiplies-to-make-196-but-adds-to-make-53\/","title":{"rendered":"What number multiplies to make 196 but adds to make 53"},"content":{"rendered":"\n

What number multiplies to make 196 but adds to make 53?<\/p>\n\n\n\n

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

To solve for two numbers that multiply to 196 and add to 53, we can use algebraic methods. Let’s denote the two numbers as (x) and (y).<\/p>\n\n\n\n

We have two equations based on the problem’s conditions:<\/p>\n\n\n\n

    \n
  1. (x \\cdot y = 196) (Equation 1)<\/li>\n\n\n\n
  2. (x + y = 53) (Equation 2)<\/li>\n<\/ol>\n\n\n\n

    Step 1: Express One Variable in Terms of the Other<\/h3>\n\n\n\n

    From Equation 2, we can express (y) in terms of (x):
    [
    y = 53 – x
    ]<\/p>\n\n\n\n

    Step 2: Substitute into the Multiplication Equation<\/h3>\n\n\n\n

    Now, we can substitute (y) into Equation 1:
    [
    x \\cdot (53 – x) = 196
    ]
    Expanding this gives:
    [
    53x – x^2 = 196
    ]<\/p>\n\n\n\n

    Step 3: Rearrange to Form a Quadratic Equation<\/h3>\n\n\n\n

    Rearranging the equation, we get:
    [
    -x^2 + 53x – 196 = 0
    ]
    To make it standard, we can multiply through by (-1):
    [
    x^2 – 53x + 196 = 0
    ]<\/p>\n\n\n\n

    Step 4: Solve the Quadratic Equation<\/h3>\n\n\n\n

    To solve this quadratic equation, we can use the quadratic formula:
    [
    x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}
    ]
    Here, (a = 1), (b = -53), and (c = 196). Plugging in these values:
    [
    x = \\frac{53 \\pm \\sqrt{(-53)^2 – 4 \\cdot 1 \\cdot 196}}{2 \\cdot 1}
    ]
    Calculating the discriminant:
    [
    (-53)^2 = 2809 \\quad \\text{and} \\quad 4 \\cdot 1 \\cdot 196 = 784
    ]
    So, the discriminant becomes:
    [
    2809 – 784 = 2025
    ]
    Taking the square root:
    [
    \\sqrt{2025} = 45
    ]
    Substituting back into the quadratic formula gives:
    [
    x = \\frac{53 \\pm 45}{2}
    ]
    Calculating the two possible values for (x):<\/p>\n\n\n\n

      \n
    1. (x = \\frac{98}{2} = 49)<\/li>\n\n\n\n
    2. (x = \\frac{8}{2} = 4)<\/li>\n<\/ol>\n\n\n\n

      Step 5: Find the Corresponding (y) Values<\/h3>\n\n\n\n

      Using (x = 49) in Equation 2:
      [
      y = 53 – 49 = 4
      ]
      Using (x = 4):
      [
      y = 53 – 4 = 49
      ]<\/p>\n\n\n\n

      Conclusion<\/h3>\n\n\n\n

      Thus, the two numbers are 49 and 4. They multiply to:
      [
      49 \\times 4 = 196
      ]
      And they add to:
      [
      49 + 4 = 53
      ]
      This verifies our solution, making the final answer: 49 and 4<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

      What number multiplies to make 196 but adds to make 53? The Correct Answer and Explanation is: To solve for two numbers that multiply to 196 and add to 53, we can use algebraic methods. Let’s denote the two numbers as (x) and (y). We have two equations based on the problem’s conditions: Step 1: […]<\/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-158835","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/158835","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=158835"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/158835\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=158835"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=158835"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=158835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}