SOLUTION: if Tom gives maria 30 cents, they will have equal amounts of money. But if Maria then gives Tom 50 cents, he will how have twice as much money as she does. how much does each have

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Question 1210503: if Tom gives maria 30 cents, they will have equal amounts of money. But if Maria then gives Tom 50 cents, he will how have twice as much money as she does. how much does each have now?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39681) About Me  (Show Source):
You can put this solution on YOUR website!
                 IF      THEN IF

Tom       t      t-30     t-30+50=t+20

Maria     m      m+30     m+30-50=m-20

Following the description given,
system%28t-30=m%2B30%2Ct%2B20=2%28m-20%29%29

Solve for original t and m money cents quantities
system%28t-m=60%2Ct%2B20=2m-40%29

system%28t-m=60%2Ct-2m=-60%29

system%28t-m=60%2C-t%2B2m=60%29
ADD those.
m=120 and then t=180

They each then have AFTER the second transfer
Tom, 200
Maria, 100

Answer by ikleyn(53354) About Me  (Show Source):
You can put this solution on YOUR website!
.
If Tom gives Maria 30 cents, they will have equal amounts of money.
But if Maria then gives Tom 50 cents, he will how have twice as much money as she does.
How much does each have now?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the amount which Tom and Maria each have equally after first exchange. 


It means that before first exchange, Tom had (x+30) cents, while Maria had (x-30) cents.


Now we consider the second exchange.  For it, we have this equation

    x + 50 = 2(x - 50)


Simplify and find x

    x + 50 = 2x - 100,

    50 + 100 = 2x - x

    x = 150.


It implies that originally (or "now")  Tom has 150+30 = 180 cents;  Maria has 150-30 = 120 cents.    ANSWER

Solved.