SOLUTION: Could u please answer this... thanks... The sum of the ages of the father and his son is 99. If the age of the son is added to the inverted age of the father the sum is 72. if t

Question 304073: Could u please answer this... thanks...
The sum of the ages of the father and his son is 99. If the age of the son is added to the inverted age of the father the sum is 72. if the inverted age of the son is subtracted from the age of the father, the difference is 22. what are their ages?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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
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