Question

The difference in Cameron and Avery’s ages is 5. The product of their ages is 104. If Cameron is older, how old is Avery?

Answer 1

• Cameron is 13 and Avery is 8 years old

Explanation:

Let Cameron's age be x and Avery's age be y.

The difference is 5 and the product is 104:

• x - y = 5
• xy = 104

Solve by substitution:

• x = y + 5

• xy = 104
• y(y + 5) = 104
• y² + 5y - 104 = 0
• y = (- 5 ± √(5² + 4*104))/2 = (- 5 ± √441)/2 = ( - 5 ± 21)/2

Taking the positive root as age can't be negative:

• y = 8

Find x:

• x = 8 + 5 = 13