Question 5955: david`s father is two year old than his mother and his mother`s age is the square of his age. They years adds up to 80 years.How old is each one of them?
Answer by glabow(165)   (Show Source):
You can put this solution on YOUR website! Define variables:
x = David's age
f = father's age
m = mother's age
We know:
f = m + 2
 = m
x + f + m = 80
Rearrange to 
Substitute m+2 for f, giving  which is 
which is  which is 
Substitute for m, giving 
Rearranging gives 
This can be solved by factoring. We are looking for two numbers that multiply to -78 and when we subtract twice one from the other we get 1. If we assume the ages are given in whole numbers, possible answers to numbers that multiply to 78 are (1, 78), (2, 39), and (6, 13). By inspection we see that 2*6 is different from 13 by 1. So the factors are either 6 and -13 or -6 and 13. Since we want a positive 1, -6 and 13 are correct. The equation factors to
 and x will be either -13 or 6.
Obviously,
x = 6
m = 36
f = 38
Checking, 
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