Three softball teams ordered equipment from the same catalog. The first team spent $285 on 5 shirts, 4 caps, and 8 bats. The second team spent $210 on 12 shirts and 6 caps. The third team spent $250 for 7 shirts, 10 caps, and 3 bats. What were the catalog prices for shirts, caps, and bats

Solution:

s=price of a shirt

c=price of a cap

b=price of a bat

285=5s+4c+8b ... (equation 1)

210=12s+6c ... (equation 2)

250=7s+10c+3b ... (equation 3)

Multiply equation 1 by 3 and Multiply equation 3 by 8

855=15s+12c+24b

2000=56s+80c+24b

subtract these equations

1145=41s+68c, now use this equation and equation 2

1145=41s+68c

210=12s+6c

multiply the top equation by 6 and the bottom equation by 68

6870=246s+408c

14,280=816s+408c

subtract these equations

7410=570s

s=7410/570=13

1 shirt cost $13.00

Using equation

210=12*13+6c

210=156+6c

210-156=6c

54=6c

c=54/6=9

1 cap cost $9.00

Using equation 1

285=5*13+4*9+8b

285=65+36+8b

285=101+8b

285-101=8b

184=8b

b=184/8=23

1 bat cost $23.00