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# 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(x + 7) = 120#

#=> x^2 + 7x = 120#

#=> x^2 + 7x - 120 = 0#

#=> (x - 8)(x + 15) = 0#

#=> x = 8, x = -15#

But #x# should be positive.

#x = 8, y = 15#