My daughter is twice as old as my son and half as old as I am. In twenty-two years my son will be half my age. How old is my daughter?

Guest Apr 25, 2015

#3**+8 **

Here's a way to do this with one variable only.

Let the son's age =x, the daughter's age = 2x, and the mother's age = 4x

And we have that in 22 years, the son wll be half as old as the mother......thus.....

2(x + 22) = 4x + 22

2x + 44 = 4x + 22

22 = 2x

x = 11 and that's the son's age

2x = 22 and that's the daughter's age

CPhill
Apr 25, 2015

#1**+8 **

m = my age, d = daughter's age, s = son's age.

d = 2s (1)

d = m/2 (2)

s + 22 = (m + 22)/2 (3)

Put (1) and (2) in (3)

d/2 + 22 = d + 11

Rearrange

d/2 = 11

d = 22

So daughter is 22.

Alan
Apr 25, 2015

#3**+8 **

Best Answer

Here's a way to do this with one variable only.

Let the son's age =x, the daughter's age = 2x, and the mother's age = 4x

And we have that in 22 years, the son wll be half as old as the mother......thus.....

2(x + 22) = 4x + 22

2x + 44 = 4x + 22

22 = 2x

x = 11 and that's the son's age

2x = 22 and that's the daughter's age

CPhill
Apr 25, 2015