SOLUTION: Three years ago, X's age was double of Y's. Seven year hence the sum of their ages will be 83 years. What is the age of X today?

Question 878521: Three years ago, X's age was double of Y's. Seven year hence the sum of their ages will be 83 years. What is the age of X today?
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
x-3 = 2(y-3) [Three years ago, X's age was double of Y's.]
x-3 = 2y-6
Add 3 to each side
x = 2y-3
(x+7) + (y+7) = 83 [Seven year hence the sum of their ages will be 83 years]
Let's work the second equation.
x+y+14 = 83
subtract 14 from each side
x+y = 69
Substitute the value of x from the first equation into the second.
(2y-3) + y = 69
3y - 3 = 69
Add 3 to each side
3y = 72
Divide each side by 3
y = 24
.
If y is 24, then x is 69 - 24, or 45.
.
Let's plug it in to make certain.
3 years ago, x's age was double y's. Three years ago, x would have been 42. Y would have been 21. That is indeed double.
Success!
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