Mathematics

Question

The product of two integers is about 50 less than one of the integers. Explain your answer. Think of three or more possible pairs of integers.

1 Answer

  • an integer is a whole number and the product of numbers means to multiply them. So so we know that:
    x * y = x - 50

    So the product (x * y) is 50 less than one of the integers ( x - 50)

    I can divide both sides by x:
    y = (x - 50) / x where x is not zero
    y = x/x - 50/x
    y = 1 - 50/ x

    x can no longer be zero since you cannot divide by zero

    the only way for y to be a whole number is if 50/x is a whole number. 50/x can onky be a whole number if x is a factor of 50. so take any factor of 50 and that will be possible answers.
    factors of 50: 1,2,5,10,25,50

    these would be possible x values. To to find corresponding y values plug in x
    y = 1 - 50/1
    y = 1 - 50
    y = -49
    So first pair is (1, -49)
    do the same for the rest and get
    (2, -24)
    (5, -9)
    (10, -4)
    (25, -1)
    (50, 0)
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