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# How old is my daughter?

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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
+81090
+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
Sort:

#1
+26412
+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
#2
+91510
+3

Thanks Alan,

These are always great puzzle questions

Melody  Apr 25, 2015
#3
+81090
+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
#4
+904
+3

impressive

HeatherF  Apr 25, 2015
#5
+1068
0

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civonamzuk  Apr 25, 2015

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