# Linear equation strange problem

1. Dec 3, 2014

### Rectifier

The problem
Adam is saving 1, 5 and 10 dollar bills. Adam has 165 bills. The amount of one dollar bills is twice as high as 10-dollar bills. The total value of his savings is 735 dollars. How many 5-dollar bills does Adam have?

This problem was translated. Sorry for grammatical errors.

The attempt at a solution
x = one dollar bills
y = five dollar bills
z = ten dollar bills

The amount of bills is:
$x+y+z=165$
We also know that:
$2x = z$ which means that the amount of bills can be rewritten as:
$x+y+2x=165 \\ y+3x=165$

The value of his savings is:
$1 \cdot x + 5 \cdot y + 10 \cdot z = 735$

I insert $2x = z$ in the second equation and get following:
$1 \cdot x + 5 \cdot y + 10 \cdot 2x = 735 \\ x + 5y + 20x = 735 \\ 5y + 21x = 735 \\$

I solve the linear equation of
$y+3x=165 \\ 5y + 21x = 735$

$7y+21x=1155 \\ 5y + 21x = 735$

$21x=1155-7y \\ 21x = 735-5y$

$735-5y=1155-7y \\ 2y=1155-735 \\ 2y= 420 \\ y = 210$
Which is clearly wrong. y (is 5 dollar bills) 5 * 210 = 1050 (but Adams value is 735)

I have tried some other methods but I cant seem to solve this problem. Please help :,(

2. Dec 3, 2014

### Staff: Mentor

To be clearer, each of the above should say "the number of ..."
No, this is wrong. What is stated is that the number of one-dollar bills is twice as large as the number of ten-dollar bills. This translates into an equation as x = 2z. You have 2x = z, which is wrong.

3. Dec 3, 2014

### Rectifier

Oh!!! Thank you for finding the error! ;D