SOLUTION: Tina is 3 years younger than Tom. The ages are in the ratio 2:3. Find their ages.

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Question 533972: Tina is 3 years younger than Tom. The ages are in the ratio 2:3. Find their ages.
Answer by Maths68(1474) About Me  (Show Source):
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Let
Present age of Tina = t
Present age of Tom = m


Tina is 3 years younger than Tom
t=m-3....(1)

The ages are in the ratio 2:3
t/m=2/3
t=2m/3........(2)

Plug in the value of t from (1) to (2)
2m/3=m-3
2m=3(m-3)
2m=3m-9
2m-3m=-9
-m=-9
Multiply by (-1) both sides
m=9
Plug in the value of m in (1)
t=m-3
t=9-3
t=6

Present age of Tina = t = 6
Present age of Tom = m = 9