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9 February, 19:31

An integer is 2 less than 4 times another. If the product of the two integers is 56, then find the integers

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Answers (2)
  1. 9 February, 19:38
    0
    -7/2 and 4

    Step-by-step explanation:

    start by using x to represent the number

    the first number is x and the 2nd number is 4 times x minus 2

    these numbers can be represented as x & 4x-2

    now since the product of the 2 numbers is 56, set x times 4x-2 equal to 56

    when you expand the equation you get

    4x^2-2x=56

    subtract 56 from the right and you have a quadratic equation. simply factor and you get the roots - 7/2 and 4
  2. 9 February, 19:51
    0
    x = 4

    y = 14

    Step-by-step explanation:

    Step one : we interpret the word problem using equations

    Let's assume the integer is y;

    and another integer is x

    4 times x = 4x

    2 less than 4 times x = 4x - 2

    The first integer, y = 4x - 2

    The product of x and y is 56

    y = 4x - 2

    x (4x - 2) = 56

    On expansion,

    4x² - 2x = 56

    The general form of a quadratic equation is

    ax² + bx + c = 0

    Step 2 : represent the equation, 4x² - 2x = 0 in the form of a quadratic equation by subtracting 56 from both sides

    4x² - 2x - 56 = 56 - 56

    4x² - 2x - 56 = 0

    Now we have a quadratic equation

    Step 3 : solve the quadratic equation, 4x² - 2x - 56 = 0

    ax² + bx + c = 0

    a x c = ac

    We find factors of ac that can be added together to give b

    4 x - 56 = - 224

    Factors of - 224 are

    1 X - 224 = - 224

    2 X - 112 = - 224

    .

    .

    .

    -16 X 14 = - 224

    -16 + 14 = - 2

    -16x + 14x = - 2x

    4x² - 16x + 14x - 56 = 0

    (4x² - 16x) + (14x - 56) = 0

    Factorise each bracket

    4x (x - 4) + 14 (x - 4) = 0

    (4x + 14) (x - 4) = 0

    4x + 14 = 0

    x - 4 = 0

    x = - 14/4

    Or

    x = 4

    Since the numbers are integers and not fractions, x = 4 is the valid solution for the statement.

    The integer, y that is 2 less than 4 times another integer x = (4 times 4) - 2 = 16 - 2 = 14
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