Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?

Let Faith's age be f. Let her mother's age be m. We're given:

1. f = m/5
2. f + m = 30

Rearrange (1) by cross-multiplying:
m = 5f

Substitute this into equation (2):
f + 5f = 30

Type this equation into our search engine and we get:
f = 5