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29 March, 09:03

The product of two positive integers plus their sum is 95. The integers are relatively prime, and each is less than 20. What is the sum of the two integers?

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  1. 29 March, 09:55
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    Let the fist integer be x, the second is x+20

    the product of the numbers is:

    x (x+20)

    the sum of the numbers is:

    x+x+20=2x+20

    the sum of the above operations will give us:

    2x+20+x^2+20x=95

    x^2+22x+20=95

    this can be written as quadratic to be:

    x^2+22x-75=0

    solving the above we get:

    x=3 and x=-25

    but since the integers should be positive, then x=3

    the second number is x+20=3+20=23

    hence the numbers are:

    3 and 23
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