# 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?

Dec 1, 2014

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

$y = x + 7$

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

$x \left(x + 7\right) = 120$

$\implies {x}^{2} + 7 x = 120$

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

$\implies \left(x - 8\right) \left(x + 15\right) = 0$

$\implies x = 8 , x = - 15$

But $x$ should be positive.

$x = 8 , y = 15$