Question

Marty made a $220 bank deposit using $10 bills and $5 bills. She gave the teller a total of 38 bills, how many $5 bills were in the deposit?
Responses
A 6 five-dollar bills6 five-dollar bills
B 28 five-dollar bills28 five-dollar bills
C 32 five-dollar bills32 five-dollar bills
D 34 five-dollar bills

Answer 1

Let's denote the number of $10 bills as \( x \) and the number of $5 bills as \( y \).

We have two equations based on the information given:
1. The total number of bills is 38:
\[
x + y = 38
\]

2. The total amount of money is $220:
\[
10x + 5y = 220
\]

Now, we can solve these equations. First, let's solve for \( x \) in terms of \( y \) from the first equation:
\[
x = 38 - y
\]

Next, we substitute \( x \) into the second equation:
\[
10(38 - y) + 5y = 220
\]

Expanding this equation gives:
\[
380 - 10y + 5y = 220
\]
\[
380 - 5y = 220
\]

Now, isolate \( y \):
\[
-5y = 220 - 380
\]
\[
-5y = -160
\]
\[
y = \frac{-160}{-5} = 32
\]

Now we have \( y = 32 \) (the number of $5 bills). To find \( x \), substitute \( y \) back into the first equation:
\[
x + 32 = 38
\]
\[
x = 38 - 32 = 6
\]

We found that there are 6 $10 bills and 32 $5 bills.

Now, checking the amounts:
- Amount from $10 bills: \( 10 \times 6 = 60 \)
- Amount from $5 bills: \( 5 \times 32 = 160 \)

The total is:
\[
60 + 160 = 220
\]

This confirms our solution is correct.

Thus, the answer is:
**C** 32 five-dollar bills.