Question 850079: When the son will be as old as his father today, the sum of their ages then will be 126. When the father was as old as his son is today, the sum of their ages then was 38. Find their present ages.
Answer by ortarico(23)   (Show Source):
You can put this solution on YOUR website! Let the ages of father and son be denoted as 'x' and 'y' respectively.
And the difference of their ages be 'z' i.e. (x-y);
x+z+y+z=126
x+y+2z=126
Recall, z=(x-y)
:.x+y+2x-2y=126
3x-y=126.......eqn1
x=126/3+y/3
x=42+y/3.......eqn2
When the father was as old as his son;
x-z+y-z=38
x+y-2z=38
Recall, z=(x-y)
x+y-2x+2y=38
-x+3y=38
x-3y=-38........eqn3
x=3y-38.........eqn4
Equating eqn2 and eqn4 to solve for y:
42+y/3=3y-38
Find the LCD of LHS and cross multiply:
126+y=9y-114
y-9y=-114-126
-8y=-240
y=30 present age of son
substitute y=30 into eqn4;
x=3(30)-38
x=90-38
x=52 present age of father
PS: In 22 yrs father would be 74, and son 52 which sum up to 126. And 22 yrs ago, father was 30, son 8 which summed up 38
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