Splitting a Delivery Fee Three Ways
A food-delivery service charges a flat $6.00 delivery fee plus a per-item tax of 8% applied only to the food subtotal (not to the delivery fee). Three coworkers order together. Ana's food items total $24.00, Ben's total $15.00, and Cara's total $11.00. They agree to split the $6.00 delivery fee equally, but each person pays the tax on their own food items. Cara insists the simplest fair method is to divide the entire final bill by 3. Ben says that method is unfair to him. The grand total comes to $60.00 before any rounding.
1. Compute each person's correct share (delivery split equally, tax on own food only). Then compute what each would pay under Cara's equal-thirds method.
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Tax rate 8% = 0.08.
- Ana: food $24.00, tax = 24.00 × 0.08 = $1.92, delivery = $6.00 ÷ 3 = $2.00 → $27.92
- Ben: food $15.00, tax = 15.00 × 0.08 = $1.20, delivery $2.00 → $18.20
- Cara: food $11.00, tax = 11.00 × 0.08 = $0.88, delivery $2.00 → $13.88 Check: 27.92 + 18.20 + 13.88 = $60.00 ✓ Equal thirds: 60.00 ÷ 3 = $20.00 each.
2. Using your numbers, explain quantitatively why Ben is right that equal thirds is unfair, and identify who gains and who loses.
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Compare each correct share to $20.00:
- Ana: 27.92 − 20.00 = +$7.92 (she underpays under equal thirds)
- Ben: 18.20 − 20.00 = −$1.80 (he overpays)
- Cara: 13.88 − 20.00 = −$6.12 (she overpays) The gains and losses balance: +7.92 − 1.80 − 6.12 = 0 ✓ Ben is correct: equal thirds makes him pay $1.80 more than his true share. Cara is the biggest loser at $6.12, so her "simplest" method actually costs her the most. The equal split only looks fair because it ignores that Ana's larger order drives most of the tax.