7. Syncere wants to purchase custom drumsticks for his 12 music students. He has two discounts. The first discount is for \( 25 \% \) off his entire purchase. The second discount is for \( \$ 5.00 \) off. Syncere has the option to apply his discounts in a different order. - Option 1:25\% off then \( \$ 5 \) off the total. Option 2: \( \$ 5 \) off, then \( 25 \% \) off the total If custom drumsticks cost \( \$ 15.95 \) per pair, which option provides the better deal by how much less?

To determine which discount option provides the better deal, let's calculate both scenarios based on the cost of the custom drumsticks. 1. **Calculating the total cost without discounts:** \[ \text{Total Cost} = \text{Price per pair} \times \text{Number of students} = 15.95 \times 12 = 191.40 \] 2. **Option 1: 25% off then $5 off** - Calculate 25% off first: \[ \text{Discount} = 191.40 \times 0.25 = 47.85 \] \[ \text{New total} = 191.40 - 47.85 = 143.55 \] - Now apply the $5 off: \[ \text{Final total} = 143.55 - 5 = 138.55 \] 3. **Option 2: $5 off then 25% off** - Apply the $5 off first: \[ \text{New total} = 191.40 - 5 = 186.40 \] - Now calculate 25% off: \[ \text{Discount} = 186.40 \times 0.25 = 46.60 \] \[ \text{Final total} = 186.40 - 46.60 = 139.80 \] 4. **Comparison:** - Option 1 total: $138.55 - Option 2 total: $139.80 To find out which option is better, subtract the totals: \[ 139.80 - 138.55 = 1.25 \] Thus, Option 1 provides the better deal by **$1.25**.