Future age
Algebra
Level
1
The ratio of Ana's age to Maria's age is . Eight years ago, Ana was 13 years older than Maria. What is the sum of their ages 10 years from now?
The answer is 59.
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1 solution
Let A be Ana's age and M be Maria's age. Then we have
M A = 1 2 ⟹ A = 2 M ( 1 )
and
A − 8 = 1 3 + M − 8 ⟹ A = 1 3 + M ( 2 )
Substitute ( 1 ) in ( 2 ) , we have
2 M = 1 3 + M
M = 1 3
It follows that A = 2 ( 1 3 ) = 2 6
The sum of their ages 1 0 years from now is A + 1 0 + M + 1 0 = 2 6 + 1 0 + 1 3 + 1 0 = 5 9