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# The product of two positive numbers is 96. Determine the two numbers if one is 4 more than the other

##### Administrator

**Staff member**

The product of two positive numbers is 96. Determine the two numbers if one is 4 more than the other.

Let the 2 numbers be x and y.

We have:

- xy = 96
- x = y - 4

__Substitute (2) into (1)__
(y - 4)y = 96

y^2 - 4y = 96

__Subtract 96 from both sides:__
y^2 - 4y - 96 = 0

__Factoring using our quadratic calculator, we get:__
(y - 12)(y + 8)

So y = 12 and y = -8. Since the problem states positive numbers, we use

**y = 12**.

Substituting y = 12 into (2), we get:

x = 12 - 4

**x = 8**
**We have (x, y) = (8, 12)**