SOLUTION: Ari is 3 times as old as Ben now. In 6 years' time, the total age of Ari and Ben will be 84 years. How old will Ben be in 6 years' time?

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Question 1167887: Ari is 3 times as old as Ben now. In 6 years' time, the total age of Ari and Ben will be 84 years. How old will Ben be in 6 years' time?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
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Ari is 3 times as old as Ben now. In 6 years' time, the total age of Ari and Ben will be 84 years. How old will Ben be in 6 years' time?
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Ari is k times as old as Ben now. In p years' time, the total age of Ari and Ben will be t years. How old will Ben be in p years' time?
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A, Ari
B, Ben

system%28A=kB%2CA%2Bp%2BB%2Bp=t%29

A=kB%2CA%2BB=t-2p

kB%2BB=t-2p
B%28k%2B1%29=t-2p
B=%28t-2p%29%2F%28k%2B1%29
How old will Ben be in p years?
B%2Bp=highlight%28%28t-2p%29%2F%28k%2B1%29%2Bp%29

Putting in the values, highlight%28B%2B6%29=%2884-2%2A6%29%2F%283%2B1%29%2B6=highlight%2824%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


By formal algebra....

x = Ben's age now
3x = Ari's age now
x+6 = Ben's age 6 years from now
3x+6 = Ari's age 6 years from now

The sum of their ages 6 years from now will be 84:
%28x%2B6%29%2B%283x%2B6%29+=+84

Solve using basic algebra; then remember the answer to the question is Ben's age 6 years from now, which is x+6 -- not just x.

Informally, using logical reasoning and simple arithmetic (good brain exercise!)....

The sum of their ages 6 years from now will be 84, so the sum of their ages now (subtract 6 years for each of them) is 72.

Since Ari is now 3 times as old as Ben, simple mental arithmetic tells us Ben is now 18 and Ari is 54.

So Ben's age 6 years from now will be 18+6=24.

If you completed solving the problem using the formal algebra method suggested above, you will see that the formal algebra used exactly the same calculations as the informal solution.