How do you find the two numbers by using the factoring method, if one number is seven more than the other and the product of two positive numbers is 120?

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Answer 1 · 2014-12-01T15:40:28

Let $x$ $x$ be the smaller number
Let $y$ $y$ be the larger number.

$y = x + 7$ $y = x + 7$

From the statement "the product of two positive numbers is 120", Assume $x > 0, y > 0$ $x > 0, y > 0$

$x (x + 7) = 120$ $x(x + 7) = 120$

$\Rightarrow x^{2} + 7 x = 120$ $=> x^2 + 7x = 120$

$\Rightarrow x^{2} + 7 x - 120 = 0$ $=> x^2 + 7x - 120 = 0$

$\Rightarrow (x - 8) (x + 15) = 0$ $=> (x - 8)(x + 15) = 0$

$\Rightarrow x = 8, x = - 15$ $=> x = 8, x = -15$

But $x$ $x$ should be positive.

$x = 8, y = 15$ $x = 8, y = 15$