Ralph’s age is currently 3 years more than twice Joe’s age. But, 3 years ago Ralph was four times as old as Joe was then. How old will Joe be in 10 years?
Question
Ralph’s age is currently 3 years more than twice Joe’s age. But, 3 years ago Ralph was four times as old as Joe was then. How old will Joe be in 10 years?
Solution
Let's denote Ralph's current age as R and Joe's current age as J.
From the problem, we have two equations:
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R = 2J + 3 (Ralph’s age is currently 3 years more than twice Joe’s age)
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R - 3 = 4(J - 3) (3 years ago Ralph was four times as old as Joe was then)
We can substitute equation 1) into equation 2) to solve for J:
2J + 3 - 3 = 4J - 12 2J = 4J - 12 2J = 12 J = 6
Substitute J = 6 into equation 1) to find R:
R = 2*6 + 3 = 15
So, Joe is currently 6 years old. In 10 years, Joe will be 6 + 10 = 16 years old.
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