Age word problem

Question

A girl has half the age of her mother, and the father is five years more than the age of the mother. If the total of their age is 100. What is the age of the father, mother and the daughter?

Answer 1

Hi Ola,

 

Let G = the girl's age and M = the mother's age and F = the father's age

 

Now let's translate the English into math . . .

 

the girl is half the age of her mother--> G = M/2 so 2G = M

 

the father is 5 years older than the mother--> F = M + 5

 

total age if 100--> G + F + M = 100

 

We have three variables and three equations so it's time to substitute

 

Substituting 2G for M in the second equation--> F = 2G + 5

 

Substituting 2G + 5 for F in the third equation and 2G for M in the third equation:

 

G + 2G + 5 + 2G = 100

 

5G + 5 = 100

 

5G = 95

 

G = 19

 

Then M = 38 and F = 43

 

Plug these values back into the problem to make sure they work.

 

Have fun.

 

Dan