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Tom planted 81 plants in his garden at a total cost of $21.85. The 81 plants consisted of peppers at 20 cents each tomatoes at 35 cents each and eggplants at 30 cents each. If the total number of peppers and tomatoes was only half the number of eggplants, then how many of each did he plant?

  • Math -

    number of tomatoes --- x
    number of peppers ---- y
    number of eggplants --- z

    x+y+z = 81 (#1)

    35x + 20y + 30z = 2185
    or
    7x + 4y + 6z = 437 (#2)

    x+y = (1/2)z
    2x + 2y = z (#3)

    plug #3 into #1
    x+y+2x+2y=81
    3x + 3y=81
    x+y = 27 --- or y = 27-x ---- #4

    plug #3 into #2
    7x + 4y + 6(2x+2y) = 437
    19x + 16y = 437 --- #5

    sub #4 into #5

    19x + 16(27-x) = 437
    3x = 5

    uggghhhh, x should be a whole number

    either I made an arithmetic error or the question is bogus.

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