Question

The age of Mary, Jo, and Larry have a sum of 120. Mary's age is three times Jo's age, and Larry's age is 5 less than Jo's age. Find the age's of Mary, Jo, and Larry. And fill in these blanks. If Mary's age is 75 then Jo's is....... and Larry's age is......

Answer 1

Assume Jo's age is x.

Mary is 3x, Larry is x-5

So x + 3x + (x-5) = 120

x = 25

So Jo is 25, Mary is 25*3 = 75, Larry is 25-5 = 20

Answer 2

Let M = Mary's age.
Let J = Jo's age
Let L = Larry's age.

The sum of their ages is 120. Therefore
M + J + L = 120 (1)

Mary's age is three times Jo's age. Therefore
M = 3J (2)

Larry's age is 5 less than Jo's age. Therefore
L = J - 5 (3)

Substitute (2) and (3) into (1).
3J + J + (J-5) = 120
3J + J + J - 5 = 120
5J - 5 = 120
5J = 120 + 5 = 125
J = 125/5 = 25

Therefore
J = 25, M = 3J = 75, L = J - 5 = 20
Answer: Mary's age = 75; Jo's age = 25; Larry's age = 20

If Mary's age is 75, then Jo's age is 25, and Larry's age is 20.