SOLUTION: A has $x and B has $y. If A gives B $3, B will have 2 times as much as A. If B gives a $6, A will have $4 more than B. How much does A have?

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Question 205842: A has $x and B has $y. If A gives B $3, B will have 2 times as much as A. If B gives a $6, A will have $4 more than B. How much does A have?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
A has $x and B has $y. If A gives B $3, B will have 2 times as much as A. If B gives A $6, A will have $4 more than B.

First, we look at:

>>...A has $x and B has $y. If A gives B $3,...<<

...then, A will have $(x-3), and B will have $(y+3)...

>>...B will have 2 times as much as A...<< 

...so $(y+3) will be 2 times $(x-3), or

             (y+3) = 2(x-3)

>>...A has $x and B has $y... If B gives A $6,...<<

...then, B will have $(y-6), and A will have $(x+6)...

>>... A will have $4 more than B...<< 

...so $(x+6) will be $(y-6)+4, or

             (x+6) = (y-6)+4

So we have this system of equations:

system%28%28y%2B3%29=2%28x-3%29%2C%28x%2B6%29=%28y-6%29%2B4%29

Simplifying:

system%28y%2B3=2x-6%2Cx%2B6=y-6%2B4%29

system%28y=2x-9%2Cx%2B6=y-2%29

system%28y=2x-9%2Cx=y-8%29

Solve by substitution and get

x=17, y=25

So A has $17 and B has $25.

Checking:

>>...If A gives B $3,...<< 

then A will have $14, and B will have $28.

>>...B will have 2 times as much as A...<<

And yes, indeed, $28 will be 2 times $14.

>>...If B gives A $6,...<<

then B will have $19, and A will have $23

>>...A will have $4 more than B...<<

And, yes indeed, $23 is $4 more than $19.

Edwin