SOLUTION: Paul's father is 2 years older than his mother. Paul's age is one third his father's age. When Paul was born, the sum of his parent's age was 42. How old are Paul's parents now?

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Question 278836: Paul's father is 2 years older than his mother. Paul's age is one third his father's age. When Paul was born, the sum of his parent's age was 42. How old are Paul's parents now?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Paul's father is 2 years older than his mother.
Paul's age is one third his father's age.
When Paul was born, the sum of his parent's age was 42.
How old are Paul's parents now?
:
Let f = father's present age
Let m = mother's present age
Let p = paul's present age
:
"Paul's father is 2 years older than his mother."
f = m - 2
or
m = f + 2
:
"Paul's age is one third his father's age."
p = 1%2F3f
:
" When Paul was born, the sum of his parent's age was 42."
(f-p) + (m-p) = 42
:
In the above equation, replace p with 1%2F3f and m with (f+2)
(f - 1%2F3f) + (f+2) - (1%2F3f) = 42
:
2%2F3f + f + 2 - 1%2F3f = 42
;
2%2F3f + f - 1%2F3f = 42 - 2
:
2%2F3f + f - 1%2F3f = 40
:
2%2F3f + 2%2F3f = 40
multiply by 3:
2f + 2f = 3(40)
4f = 120
f = 120%2F4
f = 30 yrs
and
m = 32
:
Father is 30, mother is 32
;
:
Check solution by finding P's age
1%2F3(30) = 10 yrs is Paul,s age
:
Check solution in the statement:
"" When Paul was born, the sum of his parent's age was 42."
(30-10) + (32-10) = 42