Question 1176691
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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.
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