Question 304073
Let 10x+y=age of father
Inverted age of father=10y+x
Then 99-(10x+y)=age of son, or
99-10x-y=(90-10x)+(9-y)=age of son
Inverted age of son=(90-10y)+(9-x)
Now we are told that:
10y+x+90-10x+9-y=72 simplify
9y-9x=-27 or
x-y=3------------------eq1
and
10x+y-{(90-10y)+(9-x)}=22 simplify
10x+y-90+10y-9+x=22
11x+11y=121
x+y=11-----------------eq2
add eq1 and eq2 and we get:
2x=14
x=7
substitute x=7 into eq2 and we get:
7+y=11
y=4
so father's age is 10x+y=10*7+4=74
and son's age is 99-74=25

CK
47+25=72
72=72
and
74-52=22
22=22

Hope this helps---ptaylor