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): You can put this solution on YOUR website!
Benjamin went shopping with 15 more ten-dollar notes than two-dollar
notes.
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
Answer by ikleyn(52866)   (Show Source): 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

Solved.



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