To determine which of the options is a viable solution for the number of vouchers Max bought, we can set up an equation based on the total spent, which is $175.
Let:
- \( T \) be the number of tumbling vouchers
- \( B \) be the number of boxing vouchers
The cost of the tumbling vouchers is $25 each, and the cost of the boxing vouchers is $30 each. Therefore, the equation representing the total cost is:
\[ 25T + 30B = 175 \]
Now let's evaluate each option:
-
7 tumbling vouchers and 0 boxing vouchers: \[ 25(7) + 30(0) = 175 + 0 = 175 \quad \text{(Valid)} \]
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4 tumbling vouchers and 2.5 boxing vouchers: \[ 25(4) + 30(2.5) = 100 + 75 = 175 \quad \text{(Valid)} \] However, buying half a boxing voucher is not viable, as vouchers must be whole numbers.
-
1 tumbling voucher and 5 boxing vouchers: \[ 25(1) + 30(5) = 25 + 150 = 175 \quad \text{(Valid)} \]
-
6 tumbling vouchers and 1 boxing voucher: \[ 25(6) + 30(1) = 150 + 30 = 180 \quad \text{(Invalid)} \]
Based on this evaluation, the only viable solutions that are completely valid (considering whole numbers for vouchers) are:
- 7 tumbling vouchers and 0 boxing vouchers
- 1 tumbling voucher and 5 boxing vouchers
Therefore, the valid options are the first and third ones, but since we need to choose from the provided responses, the answer is:
7 tumbling vouchers and 0 boxing vouchers.
1 answer