SOLUTION: Tom is 10 years younger than Becky. In two years, Becky will be twice as old as Tom. How old is Tom now?

Question 1176691: Tom is 10 years younger than Becky. In two years, Becky will be twice as old as Tom. How old is Tom now?
Found 2 solutions by math_tutor2020, MathTherapy:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

T = Tom's age right now
B = Becky's age right now

"Tom is 10 years younger than Becky" means
T = B-10
Whatever Becky's age is, we subtract off 10, to get Tom's age.

For instance, let's say she's 37. That would mean we plug B = 37 into the equation
T = B-10
T = 37-10
T = 27
So Tom is 27
These values may or may not be part of the answer. This is just an example.

Becky's future age in two years = B+2
Tom's future age in two years = T+2

Based on this quote
"In two years, Becky will be twice as old as Tom"
we can form the equation
B+2 = 2*(T+2)
The format is
Becky's age = 2*(Tom's age)
but this only applies at this point in the future

What we can do from here is plug the first equation into the second one
B+2 = 2*(T+2)
B+2 = 2*(B-10+2) ... replace T with B-10; since T = B-10
B+2 = 2(B-8)
B+2 = 2B-16
B-2B = -16-2
-B = -18
B = 18
Becky is currently 18 years old.

T = B-10
T = 18-10
T = 8
Tom is currently 8 years old.

Fast forward two years into the future and we have
Becky's future age = B+2 = 18+2 = 20
Tom's future age = T+2 = 8+2 = 10
We can see that Becky is twice as old as Tom at this point. We've confirmed the answers.

Answer: Tom is currently 8 years old.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Tom is 10 years younger than Becky. In two years, Becky will be twice as old as Tom. How old is Tom now?

Difference in ages: 10 years, with Becky being the older of the 2
Therefore, when Tom is Becky's age - the age that she was when he was born - Becky will be twice his age
Thus, in 2 years, Becky will be 20, and Tom' will be 10.
Two years earlier (now), Tom is:
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