SOLUTION: Charlie was buying things for his holiday party. He spent one-third of what he had plus $3 on plates and tablecloths, then one-third of what was left plus $2 on food, then half of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Charlie was buying things for his holiday party. He spent one-third of what he had plus $3 on plates and tablecloths, then one-third of what was left plus $2 on food, then half of       Log On


   

Question 607242: Charlie was buying things for his holiday party. He spent one-third of what he had plus $3 on plates and tablecloths, then one-third of what was left plus $2 on food, then half of what was left plus $10 on soda. He then had $10 left for potato chips and other snacks. How much did he start with?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE ALGEBRA WAY:
Charlie started with x (in $ units).
He spent $%281%2F3%29x%2B3 on plates and tablecloths.
After buying the plates and tablecloths he had
$x-%28%281%2F3%29x%2B3%29=x-%281%2F3%29x-3=%282%2F3%29x-3 left, and went to buy food.
He spent 1/3 of the amount above plus $2 on food.
After buying the food he had 1/3 of the amount above minus $2.
He had $%282%2F3%29%282x%2F3-3%29-2=4x%2F9-2-2=4x%2F9-4 left, and went to buy soda.
He spent 1/2 of the amount above plus $10 from the other 1/2 on soda.
So, after buying the soda he had 1/2 of the amount above minus $10.
He had $%281%2F2%29%284x%2F9-4%29-10=2x%2F9-2-10=2x%2F9-12 and that was the $10 left for chips and snacks.
highlight%282x%2F9-12=10%29
2x%2F9-12=10 --> 2x%2F9=12%2B10 --> 2x%2F9=22 --> x%2F9=11 --> highlight%28x=99%29
Charlie started with $99.

VERIFICATION:
One third of $99 plus $3 is $$33+$3=$36 spent on plates and tablecloths.
That leaves $99-$36=$63.
One third of $63 plus $2 is $21+$2=$23 spent on food.
That leaves $63-$23=$40.
One half of $40 plus $10 is $20+$10=$30 spent on soda.
That left $40-$30=$10 for chips and snacks.

THE FIFTH GRADER SOLUTION:
The final $10 left after buying the soda is $10 less that half what Charlie had before, so $20 is half what Charlie had before, and $40 is hat Charlie had before buying the soda.
The $40 amount left before buying the soda, but after buying the food is $2 less than two thirds of what Charlie had before, so $42 is two thirds of what Charlie had before. That means that $42/2=$21 is one third of what Charlie had before, and 3($21)=$63 is what Charlie had before buying the food.
The $63 amount left before buying the food, but after buying the plates and tablecloths is $3 less than two thirds of what Charlie had originally, so $63+$3=$66 is two thirds of what Charlie had originally. That means that $66/2=$33 is one third of what Charlie had originally, and 3($33)=$99 is the amount Charlie started with.