Verified Answer :

"b is three times as old as c" means that b = 3c

Add 6 years to each age to get b+6 and c+6; at this point b will be twice as old as c. So this means b+6 = 2(c+6)

Let's use substitution to solve.

b+6 = 2(c+6)

3c+6 = 2(c+6) .... replaced b with 3c

3c+6 = 2c+12

3c-2c = 12-6

c = 6

Person C is currently 6 years old.

b = 3c = 3*6 = 18

Person B is currently 18 years old.

Add 6 to each age:

b+6 = 18+6 = 24

c+6 = 6+6 = 12

Notice the jump from 12 to 24 is "times 2" which shows that person B would have a future age twice that of person C, when we fast-forward the clock 6 years into the future. This confirms we have the correct ages.

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Answers:

b = 18 years old currently

c = 6 years old currently

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