Question

Two positive numbers have a difference of 4 and a product of 96. What are the numbers?

A. 12 and 8
B. 16 and 6
C. 16 and 12
D. 18 and 14

Answer 1

The answer is A. 12 and 8

x - y = 4
x * y = 96
_____
x = y + 4
x * y = 96
______
(y + 4) * y = 96
y² + 4y = 96
y² + 4y - 96 = 0
y² + 12y - 8y - 96 = 0
(y² + 12y) - (8y + 96) = 0
y(y + 12) - 8(y + 12) = 0
(y + 12)(y - 8) = 0
y + 12 = 0 or y - 8 = 0
y = -12 or y = 8

Since, the numbers are positive, then the only solution for y is 8.

x - y = 4
y = 8
x - 8 = 4
x = 8 + 4
x = 12