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?

Question

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?

Answer 1

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.

Answer 2

To solve this problem, we can use a system of equations.

Let's assume that Tom planted p peppers, t tomatoes, and e eggplants.

1. From the given information, we know that the total number of plants Tom planted is 81:
p + t + e = 81 -- Equation 1

2. We also know that the total cost of all the plants is $21.85:
0.20p + 0.35t + 0.30e = 21.85 -- Equation 2

3. According to the problem, the number of peppers and tomatoes combined is half the number of eggplants:
p + t = (1/2)e -- Equation 3

Now, let's solve the system of equations to find the values of p, t, and e.

From Equation 3, we can rewrite it as:
2p + 2t = e

Substitute this value of e in Equation 1:
p + t + 2p + 2t = 81
3p + 3t = 81
p + t = 27 -- Equation 4

Now we have two equations in two variables (Equation 2 and Equation 4). Let's solve this system of equations.

From Equation 4, we can express p = 27 - t.

Substitute this value of p in Equation 2:
0.20(27 - t) + 0.35t + 0.30e = 21.85
5.4 - 0.20t + 0.35t + 0.30e = 21.85
0.15t + 0.30e = 16.45 -- Equation 5

Multiply Equation 4 by 0.15 to make the coefficients of t the same:
0.15p + 0.15t = 4.05

Now substitute the value of p from Equation 4 in the above equation:
0.15(27 - t) + 0.15t = 4.05
4.05 - 0.15t + 0.15t = 4.05
4.05 = 4.05

The equation is satisfied, which means there are infinitely many solutions.

Hence, we cannot determine the specific number of peppers, tomatoes, and eggplants that Tom planted based on the given information.