To determine which option is a viable solution for the number of vouchers Max bought, we can start by setting up an equation based on the total amount spent, which is $175.
Let \( T \) be the number of tumbling vouchers and \( B \) be the number of boxing vouchers. The costs are as follows:
- Each tumbling voucher: $25
- Each boxing voucher: $30
Thus, the equation representing the total cost is:
\[ 25T + 30B = 175 \]
Now, we can evaluate each response option:
-
4 tumbling vouchers and 2.5 boxing vouchers
- Total cost: \( 25(4) + 30(2.5) = 100 + 75 = 175 \) ✔ (This is a viable solution, but typically you can't purchase half a voucher.)
-
7 tumbling vouchers and 0 boxing vouchers
- Total cost: \( 25(7) + 30(0) = 175 + 0 = 175 \) ✔ (This is a viable solution.)
-
6 tumbling vouchers and 1 boxing voucher
- Total cost: \( 25(6) + 30(1) = 150 + 30 = 180 \) ✘ (This exceeds $175.)
-
1 tumbling voucher and 5 boxing vouchers
- Total cost: \( 25(1) + 30(5) = 25 + 150 = 175 \) ✔ (This is also a viable solution.)
Based on the calculations, the viable solutions are:
- 7 tumbling vouchers and 0 boxing vouchers
- 1 tumbling voucher and 5 boxing vouchers
Since the original responses provided included an option with half vouchers, the best viable option (assuming whole vouchers only) among the provided choices is:
- 7 tumbling vouchers and 0 boxing vouchers
- 1 tumbling voucher and 5 boxing vouchers
If strictly looking for whole numbers, either of the last two responses is correct.
1 answer