On her way to a concert, Hermione stopped at a restaurant for dinner. In her purse, she had 12 bills worth a total of $40. She had only $1 bills and $5 bills. How many $5 bills did Hermione have in her purse?

Question

1
2
5
7

Answer 1

Let \( x \) be the number of $1 bills and \( y \) be the number of $5 bills. We are given two equations based on the information provided:

1. The total number of bills: \[ x + y = 12 \]

2. The total value of the bills: \[ 1x + 5y = 40 \]

Now we can solve these equations step by step.

From the first equation, we can express \( x \) in terms of \( y \): \[ x = 12 - y \]

Next, we substitute \( x \) in the second equation: \[ 1(12 - y) + 5y = 40 \] This simplifies to: \[ 12 - y + 5y = 40 \] \[ 12 + 4y = 40 \] Subtract 12 from both sides: \[ 4y = 28 \] Now divide by 4: \[ y = 7 \]

Now that we have \( y \), we can find \( x \): \[ x = 12 - y = 12 - 7 = 5 \]

Thus, Hermione has:

• 5 $1 bills
• 7 $5 bills

The answer to how many $5 bills Hermione had is: \[ \boxed{7} \]