Two sisters, Mary and Jane have a total age of 98. When Mary was Jane's age, Jane was half as old as Mary is now. What are their ages?"
Let M = Mary's age now
Let J = Jane's age now
Let x be the number of years ago it was when Mary was Jane's age
Mary and Jane have a total age of 98.
That says
M + J = 98
When Mary was Jane's age
That says "x years ago Mary was Jane's age now"
M - x = J
Jane was half as old as Mary is now
That says "x years ago Jane was M
J - x = M
So we have this system of three equations in three unknowns:
If you don't know how to solve that system, post again asking how.
Answer: J = 42, M = 56, x = 14.
Checking:
Mary and Jane have a total age of 98.
That checks because 56 + 42 = 98
When Mary was Jane's age,
x = 14 years ago Mary was 56 - 14 or 42, Jane's age now. That checks.
Jane was half as old as Mary is now.
x = 14 years ago, Jane was 42 - 14 or 28, and indeed 28 is half as old as
56, Mary's present age.
So that is correct.
Edwin