Question

Which system of equations best represents the situation below?A farmer grew his own tomatoes (a), eggplants (b), and potatoes (c). Hedecided to package his vegetables and price them as follows:1 tomato, 1 eggplant, 2 potatoes for $102 tomatoes, 1 eggplant, 3 potatoes for $144 tomatoes, 3 eggplants, 5 potatoes for $20

Answer 1

- The cost of the crops are $(a) for tomatoes, $(b) for eggplants, and $(c) for potatoes.

- We simply need to follow the statements about the farmer's pricing in order to determine the correct set of equations.

Statement 1:

- "1 tomato, 1 eggplant, 2 potatoes for $10"

- If there is 1 tomato, it implies that, this tomato is priced at $(a). Similarly, 1 eggplant would be priced at $(b), but 2 potatoes would be $(c) + $(c) = $2(c).

- We are told that the total cost for this package is $10.

- Thus, the first equation must be:

`a+b+2c=10`

- We can interprete the other packages in a similar manner.

Statement 2:

"2 tomatoes, 1 eggplant, 3 potatoes for $14"

- This implies that the farmer would price the packages as follows:

2 tomatoes: 2(a)

1 eggplant: 1(b)

3 potatoes: 3(c)

- Since the total cost is $14, we can write the second equation as follows:

`2a+b+3c=14`

Statement 3:

"4 tomatoes, 3 eggplants, 5 potatoes for $20"

- This implies that the farmer would price the packages as follows:

4 tomatoes: 4(a)

3 eggplants: 3(b)

5 potatoes: 5(c)

- Since the total cost is $20, we can write the third equation as follows:

`4a+3b+5c=20`

Final Answer

The 3 equations are:

`\begin{gathered} a+b+2c=10 \\ 2a+b+3c=14 \\ 4a+3b+5c=20 \end{gathered}`

OPTION C