Max earned $175.00 mowing yards during spring break. They used the money to buy vouchers for both tumbling and boxing classes. Each tumbling class voucher cost $25.00, while each boxing class voucher cost $30.00. Which of the following is a viable solution for the number of vouchers Max bought, assuming they spent their entire earnings?(1 point)

Question

Responses

1 tumbling voucher and 5 boxing vouchers
1 tumbling voucher and 5 boxing vouchers

6 tumbling vouchers and 1 boxing voucher
6 tumbling vouchers and 1 boxing voucher

7 tumbling vouchers and 0 boxing vouchers
7 tumbling vouchers and 0 boxing vouchers

4 tumbling vouchers and 2.5 boxing vouchers

Answer 1

To find out which of the options represents a viable solution for the number of vouchers Max bought, we'll need to set up an equation based on the total money spent on tumbling and boxing classes.

Let:

• \( t \) = number of tumbling vouchers
• \( b \) = number of boxing vouchers

The total money spent can be represented as: \[ 25t + 30b = 175 \]

Now, let's check each option to see if it satisfies the equation:

1. 1 tumbling voucher and 5 boxing vouchers: \[ 25(1) + 30(5) = 25 + 150 = 175 \] ✔️ (This option is valid)

2. 6 tumbling vouchers and 1 boxing voucher: \[ 25(6) + 30(1) = 150 + 30 = 180 \] ✖️ (This option is invalid)

3. 7 tumbling vouchers and 0 boxing vouchers: \[ 25(7) + 30(0) = 175 + 0 = 175 \] ✔️ (This option is valid)

4. 4 tumbling vouchers and 2.5 boxing vouchers: \[ 25(4) + 30(2.5) = 100 + 75 = 175 \] ✔️ (However, you cannot buy half of a boxing voucher, so this option is invalid in the context of real purchases)

Based on this analysis, the viable solutions from the provided options are:

• 1 tumbling voucher and 5 boxing vouchers
• 7 tumbling vouchers and 0 boxing vouchers

Thus, the viable solutions are options 1 and 3.