Question

Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?

Answer 1

lt x years ago Sally's mother's age ie three times Sally.

80-x=3(54-x)
solve for x.

Answer 2

Sally's age is 26 less than her mother's age because 80 - 54 = 26. In other words, Sally is 26 years younger than her mother.
We can say S = M - 26; this will always be true, even if we go back any number of years.
We want to find the age at which Sally's mother, M, was 3 times Sally's age or
3S = M
At this point in time, it would still be true that
S = M - 26
The trick is to find values of S and M such that both statements are true:
3S = M AND S = M - 26

Given that S = M - 26, we can use substitution to replace "S" in the first equation with (M - 26) and then solve for M:
3(M - 26) = M
3M - 78 = M
2M = 78
M = ???
It would then be obvious how many years ago that was, compared to M's current age of 80