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