Kathie
posted by Mathematics .
In four years' time, a father will be three times as old as his son. Six years ago, he was seven times as old as his son. How old are they now? Explain your workings. Thanks

son's present age: x
father's present age : y
4 yrs from now:
son : x+4
father : y+4
y+4 = 3(x+4)
y = 3x + 8
6 yrs ago:
son : x6
father: y6
y  6 = 7(x6)
y = 7x 36
so 7x 36 =3x+8
4x = 44
x = 11
y = 3(11)+8 = 41
The son is now 11 and the father is now 41
check:
4 yrs from now: son 15, father 45
3 times as old? yes
6 yrs ago: son  5, father 35
7 times as old? yes
all is good 
Thank you very much Reiny!