Question 317673: When the son will be as old as father today, their ages will add up to 126 years. When the father was as old as the son is today, their ages add to 38 years. Find their present ages.
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! Let x = son's current age
Let y = father's current age
Equation 1 (we have to go forward (y-x) years, so we add the (y-x) terms):
[Father's new age] + [Son's new age] = 126
[y+(y-x)] + [(x + (y-x))] = 126
2y - x + y = 126
3y - x = 126
Where does the(y-x) term come from? Well, it says 'when the son will be as old as the father is today', which means that the son has to age a certain amount of years. How many years does he have to age? The difference between his current age and his father's current age. For example, if the son was 10 and the father was 40, it would take the son 30 years (or y-x = 40-10) to reach his current age. In the meantime, the father would age the same amount (y-x=40-10=30 years).
Equation 2 ( we have to go back (y-x) years, so we subtract the (y-x) terms ):
[Father's previous age] + [Son's previous age] = 38
[y - (y-x)] + [x - (y-x)] = 38
x + x - y + x = 38
3x - y = 38
y = 3x - 38
Now sub this value of y into Equation 1:
3(3x-38) - x = 126
9x - 114 - x = 126
8x = 240
x = 30
y = 3x - 38
y = 3(30) - 38
y = 52
The son is 30 years old, and the father is 52 years old.
Hope this makes sense! Let me know if it doesn't...
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