Question

You have ones and tens in your pocket. If you have 18 bills worth a total of $108, how many tens and how many ones do you have?

Answer 1

Let \( x \) be the number of ten-dollar bills and \( y \) be the number of one-dollar bills. We can set up the following system of equations based on the information given:

1. The total number of bills:
\[
x + y = 18
\]

2. The total value of the bills:
\[
10x + 1y = 108
\]

Now we can solve this system of equations.

From the first equation, we can express \( y \) in terms of \( x \):
\[
y = 18 - x
\]

Next, substitute \( y \) into the second equation:
\[
10x + (18 - x) = 108
\]

Simplifying this:
\[
10x + 18 - x = 108
\]
\[
9x + 18 = 108
\]
\[
9x = 108 - 18
\]
\[
9x = 90
\]
\[
x = 10
\]

Now we can find \( y \):
\[
y = 18 - x = 18 - 10 = 8
\]

Thus, we have:
- The number of ten-dollar bills (\( x \)) is \( 10 \).
- The number of one-dollar bills (\( y \)) is \( 8 \).

To verify, we can check the total value:
\[
10 \times 10 + 1 \times 8 = 100 + 8 = 108
\]
And the total number of bills:
\[
10 + 8 = 18
\]

Both checks are correct. Therefore, the solution is:
- **10 ten-dollar bills**
- **8 one-dollar bills**