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?

Question

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.