SOLUTION: Benjamin went shopping with 15 more ten-dollar notes than two-dollar notes. He paid $270 for a jacket with some ten-dollar notes. In the end, the number of ten-dollar notes he had
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-> SOLUTION: Benjamin went shopping with 15 more ten-dollar notes than two-dollar notes. He paid $270 for a jacket with some ten-dollar notes. In the end, the number of ten-dollar notes he had
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Question 1203169: Benjamin went shopping with 15 more ten-dollar notes than two-dollar notes. He paid $270 for a jacket with some ten-dollar notes. In the end, the number of ten-dollar notes he had left was 1/3 of the number of two-dollar notes he had left. How much money did he have at first? Found 2 solutions by mccravyedwin, ikleyn:Answer by mccravyedwin(408) (Show Source):
Let x = the number of two-dollar notes he had at first.
Let y = the number of ten-dollar notes he had at first.
...15 more ten-dollar notes than two-dollar notes...
So y = x+15
He paid $270 for a jacket with some ten-dollar notes.
After buying the jacket he had y-27 ten-dollar notes.
In the end, the number of ten-dollar notes he had left was 1/3 of the number
of two-dollar notes he had left.
So in the end he had x two-dollar notes because he didn't spend any.
y-27 = (1/3)x
x+15-27 = (1/3)x
x-12 = (1/3)x
3x-36 = x
2x = 36
x = 18
y = x+15 = 18+15 = 33
How much money did he have at first?
He had 18 two-dollar notes and 33 ten-dollar notes at first.
Edwin
You can put this solution on YOUR website! .
Benjamin went shopping with 15 more ten-dollar notes than two-dollar notes.
He paid $270 for a jacket with some ten-dollar notes.
In the end, the number of ten-dollar notes he had left was 1/3
of the number of two-dollar notes he had left.
How much money did he have at first?
~~~~~~~~~~~~~~~~~~~~
x of two-dollars notes and (x+15) of ten-dollars notes originally.
After paying $270 by ten-dollar notes, the number of remaining ten-dollar notes is ((x+15)-27) = x-12.
We are given = .
Cross-multiply, simplify and find x
3*(x-12) = x
3x - 36 = x
3x - x = 36
2x = 36
x = 36/2 = 18.
Thus originally, Benjamin went shopping with 18 two-dollars notes and 18+15 = 33 ten-dollar notes.
Hence, originally Benjamin had 10*33 + 2*18 = 366 dollars. ANSWER
