A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $15.50. Another customer buys 3 hot dogs and 2 bags of potato chips for $9.00. Find the cost of each item.

Let h represent the cost of hot dogs and p represent the cost of potato chips.

Customer 1: 4h + 5p = 15.50 ⇒ 3 (4h + 5p = 15.50) ⇒ 12h + 15p = 46.50

Customer 2: 3h + 2p = 9.00 ⇒ - 4 (3h + 2p = 9.00) ⇒ - 12h - 8p = - 36.00

7p = 10.50

p = 1.50

Customer 2: 3h + 2p = 9.00 → 3h + 2 (1.50) = 9.00 → 3h + 3.00 = 9.00 → 3h = 6.00 → h = 2.00

Answer: hot dog = $1.50, potato chips = $2.00