SOLUTION: $3000 are divided between two sons so that the elder son receives $200 more than two-thirds the share of the younger son. How much does each receives? Please help!!!!! Thank you

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Question 189683: $3000 are divided between two sons so that the elder son receives $200 more than two-thirds the share of the younger son. How much does each receives?
Please help!!!!! Thank you for saving my life!!:):):)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let
x=amount of money that the elder son receives and
y=amount of money that the younger son receives


Because $3000 is being split among the two, this means that x%2By=3000 (ie if you add their shares together, you will get $3000)

Also, since "$3000 are divided between two sons so that the elder son receives $200 more than two-thirds the share of the younger son", this tells us that x=%282%2F3%29y%2B200


x%2By=3000 Start with the first equation.


%282%2F3%29y%2B200%2By=3000 Plug in x=%282%2F3%29y%2B200


cross%283%29%28%282%2Fcross%283%29%29y%29%2B3%28200%29%2B3%28y%29=3%283000%29 Multiply EVERY term by the LCD 3 to clear the fractions.


2y%2B600%2B3y=9000 Multiply.


5y%2B600=9000 Combine like terms on the left side.


5y=9000-600 Subtract 600 from both sides.


5y=8400 Combine like terms on the right side.


y=%288400%29%2F%285%29 Divide both sides by 5 to isolate y.


y=1680 Reduce.


So this means that the younger son received $1,680


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x=%282%2F3%29y%2B200 Go back to the second equation


x=%282%2F3%29%281680%29%2B200 Plug in y=1680


x=3360%2F3%2B200 Multiply


x=1120%2B200 Reduce


x=1320 Combine like terms.



So the elder son received $1,320