Comparing Catering Bids with Tax and Discount
A school club has $1,200 for a banquet for 80 guests. Vendor A charges $12.50 per person plus a $75 setup fee and offers a 10% discount on the food subtotal only. Vendor B charges $11.75 per person plus a $150 setup fee and adds 7% sales tax to the entire bill. Vendor A's quote is tax-exempt. The club also must reserve $180 for decorations from the same $1,200 budget. The club wants the lowest total cost that stays within budget and does not want to reduce the guest count.
1. Compute the total cost for each vendor, including decorations, and state which vendor the club can afford.
Read the worked answer
Vendor A: food = 80 × 12.50 = 1,000. Discount = 10% of 1,000 = 100, so food after discount = 900. Add setup 75 = 975. Tax-exempt. Add decorations 180 = 1,155. Vendor B: food = 80 × 11.75 = 940. Add setup 150 = 1,090. Tax = 7% of 1,090 = 76.30. Total = 1,166.30. Add decorations 180 = 1,346.30. Only Vendor A fits the $1,200 budget; B exceeds it by $146.30.
2. How much money remains if the club chooses the affordable vendor? Show the subtraction and explain what the remainder does or does not allow.
Read the worked answer
1,200 - 1,155 = 45. The club has $45 left. That is not enough to add another guest at Vendor A's effective per-person food cost after the discount is $11.25, so $45 could cover up to four more guests at the discounted food rate, but the problem says the guest count is fixed. The remainder is a small cushion for incidental costs, not a major expansion.
3. If 10 more guests are added (90 total), does the vendor choice change? Support with calculations.
Read the worked answer
Vendor A: 90 × 12.50 = 1,125. Discount = 112.50; food = 1,012.50. Add 75 = 1,087.50. Add decorations 180 = 1,267.50. Vendor B: 90 × 11.75 = 1,057.50. Add 150 = 1,207.50. Tax = 7% of 1,207.50 = 84.525, about 84.53; total = 1,292.03. Add decorations 180 = 1,472.03. Neither fits $1,200. So the choice changes: at 90 guests, the club cannot afford either vendor without cutting decorations or finding more money.