Question 1092511: Sean is 20 and his brother is 12 how many years ago was sean three times as old as his brother
Answer by DrSteve(7)   (Show Source):
You can put this solution on YOUR website! I love problems like this! They're like wacky puzzles!
So lets set this one up:
what number, subtracted from BOTH THEIR AGES, will result in a number that makes Sean's age three times his brother's?
let's call Sean "S" and his brother "B" for the general equation, then we'll solve it. The number of years we're subtracting we'll just call "x".
S-x = 3(B - x)
in other words, Sean's age minus a number, is equal to 3 times Brother's age minus the same number.
We know Sean and Brother's ages, though, so let's plug them in!
20 - x = 3(12 - x)
expanding the parenthetical gives us
20 - x = 36 - 3x
now add x to both sides
20 = 36 - 2x
subtract 36 from both sides
-16 = -2x
divide both sides by -2
8 = x
...which is your answer!
You can check it thusly:
20 - 8 = 12
12 - 8 = 4
12/4 = 3 and there you go!
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