Question

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)
Responses

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
4 tumbling vouchers and 2.5 boxing vouchers

1 tumbling voucher and 5 boxing vouchers

Answer 1

To determine which of the provided options is a viable solution for the number of vouchers Max bought, we'll set up an equation based on the total amount spent.

Let \( T \) represent the number of tumbling class vouchers and \( B \) represent the number of boxing class vouchers. The cost of the tumbling vouchers is $25.00 each and the cost of the boxing vouchers is $30.00 each. Max spent a total of $175.00, so we can write the equation:

\[ 25T + 30B = 175 \]

Now let's evaluate each of the options provided:

1. **6 tumbling vouchers and 1 boxing voucher**:
\[ 25(6) + 30(1) = 150 + 30 = 180 \] (not valid, exceeds $175)

2. **7 tumbling vouchers and 0 boxing vouchers**:
\[ 25(7) + 30(0) = 175 + 0 = 175 \] (valid)

3. **4 tumbling vouchers and 2.5 boxing vouchers**:
\[ 25(4) + 30(2.5) = 100 + 75 = 175 \] (valid, but cannot buy half a boxing voucher)

4. **1 tumbling voucher and 5 boxing vouchers**:
\[ 25(1) + 30(5) = 25 + 150 = 175 \] (valid)

From these calculations, we find:
- Option 1: Invalid (total exceeds $175)
- Option 2: Valid
- Option 3: Invalid (cannot have half a boxing voucher)
- Option 4: Valid

Thus, the viable options for the number of vouchers Max bought, assuming they spent their entire earnings, are:
- 7 tumbling vouchers and 0 boxing vouchers
- 1 tumbling voucher and 5 boxing vouchers

**The correct answers based on provided options are:**
- 7 tumbling vouchers and 0 boxing vouchers
- 1 tumbling voucher and 5 boxing vouchers