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15 March, 14:56

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

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  1. 15 March, 17:35
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    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
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Home » Business » 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.
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