Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. Wh | MathCelebrity Forum

# Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. Wh

#### math_celebrity

Staff member
Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina?

Assumptions and givens:
• Let Justin's age be j
• Let Martina's age be m
• j > m (since Justin is older than Martina)

We're given the following equations :
1. j - m = 22
2. j + m = 54
Since the coefficients of m are opposites, we can take a shortcut using the elimination method and add equation (1) to equation (2)
(j + j) + (m - m) = 22 + 54
2j = 76

To solve for j, we type this equation into our math engine and we get:
j = 38

The question asks for Martina's age (m), so we can pick equation (1) or equation (2). Let's use equation (1):
38 - m = 22

To solve this equation for m, we type it in our math engine and we get:
m = 16