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One positive number is 5 less than twice a second number, and their product is 117. Find the two numbers.

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  1. 13 May, 06:04
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    x, y - the numbers

    one positive number is 5 less than twice a second number

    (1) x - 5 = 2y

    their product is 117

    (2) xy = 117

    (1) x - 5 = 2y add 5 to both sides

    x = 2y + 5 substitute it to (2)

    (2y + 5) y = 117 use distributive property

    (2y) (y) + (5) (y) = 117

    2y² + 5y = 117 subtract 117 from both sides

    2y² + 5y - 117 = 0

    2y² + 18y - 13y - 117 = 0

    2y (y + 9) - 13 (y + 9) = 0

    (y + 9) (2y - 13) = 0 ↔ y + 9 = 0 ∨ 2y - 13 = 0

    y + 9 = 0 subtract 9 from both sides

    y = - 9

    2y - 13 = 0 add 13 to both sides

    2y = 13 divide both sides by 2

    y = 6.5

    substitute the values of y to (1)

    x = 2 (-9) + 5 = - 18 + 5 = - 13 < 0

    x = 2 (6.5) + 5 = 13 + 5 = 18

    Answer: x = 18 and y = 6.5
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