A father, being asked his age and that of his son, said,

"If you add 4 to my age and divide the sum by 4, you will have my son's age.

But 6 years ago I was 7 .5 times as old as my son."

find their ages.

:

Let f = father's age now; s = son's age now

:

"If you add 4 to my age and divide the sum by 4, you will have my son's age."

 = s

Multiply equation by 4

f + 4 = 4s

f = 4s - 4

:

"But 6 years ago I was 7 .5  times as old as my son."

f - 6 = 7.5(s - 6)

f - 6 = 7.5s - 45

f = 7.5s - 45 + 6

f = 7.5s - 39

Substitute (4s-4) for f in the above equation

4s - 4 = 7.5s - 39

-4 + 39 = 7.5s - 4s

35 = 3.5s

s = 

s = 10 yrs old is the son

then

f = 4(10) - 4

f = 36 yrs old is the father:

:

:

Check solution in the statement:

"If you add 4 to my age and divide the sum by 4, you will have my son's age."

 = 10; confirms our solution