Question

Which system of equations best represents the situation below?

A farmer grew his own tomatoes (a), eggplants (b), and potatoes (c). He decided to package his vegetables and price them as follows:
2 tomatoes, 1 eggplant, 3 potatoes for $10
3 tomatoes, 2 eggplants, 4 potatoes for $14
4 tomatoes, 2 eggplants, 6 potatoes for $20

Answer 1

A.

2a +b+3c =10

3a+2b+4c=14

4a+2b+6c=20

Explanation:

Hi, to answer this question we have to write a system of equation with the information given:

The price of each package will be equal to sum of the products of each vegetable (a,b or c) and their respective amount :

So:

• 2 tomatoes, 1 eggplant, 3 potatoes for $10

2a +1b+3c =10

• 3 tomatoes, 2 eggplants, 4 potatoes for $14

3a+2b+4c=14

• 4 tomatoes, 2 eggplants, 6 potatoes for $20

4a+2b+6c=20

The system is:

2a +b+3c =10

3a+2b+4c=14

4a+2b+6c=20

(option A)

Feel free to ask for more if needed or if you did not understand something.