Math
posted by Kim on .
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?

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 = 27x  #4
plug #3 into #2
7x + 4y + 6(2x+2y) = 437
19x + 16y = 437  #5
sub #4 into #5
19x + 16(27x) = 437
3x = 5
uggghhhh, x should be a whole number
either I made an arithmetic error or the question is bogus.