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
