Question

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.

Answer 1

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