Question

A woman is 10 times as old as her daughter. In 8 years she will be 4 times as old as her daughter. How old is the mother now?

Answer 1

80 years

Explanation:

Let daughter's age be x years.

Therefore, women's age = 10x years

8 years after:

Daughter's age = (x + 8) years

Women's age = 4(x + 8) years

`4(x + 8) = (x + 8) \\ 4x + 32 = x + 8 \\ 4x - x8 - 32 \\ 3x = - 24 \\ x = ( - 24)/(3) \\ x = - 8 \\ \because \: age \: of \: a \: person \: can \: not \: be \: negative \\ \therefore \: x = 8 \\ \therefore \: 10x = 10 * 8 \\ \huge \red{ \boxed{\therefore \: 10x = 80 \: years}}`

Answer 2

Mom is 40 and her daughter is 4; in eight years, mom will be 48 and her daughter will be 12.

Explanation: