Stacey throws two dice. The difference in face value between the two dice is three, and the product of the numbers thrown is equal to twice the sum of the two numbers. Show and solve an alebraic equation that finds the numbers Stacey threw.

Answer 1

Let a be the larger number.

a - b = 3
a*b = 2(a + b)
a*(a-3) = 2a + 2(a-3)
a^2 -3a = 2a + 2a -6
a^2 -7a +6 = 0
(a - 6)(a -1) = 0
a = 6 or 1
Forget the a = 1 solution, because b cannot be negative
a = 6 and b = 3