Write a system of equations using the information given

Question

Each carton of food will feed 30 people, while each carton of clothing will help 6 people. Each 20 ft.³ box of food weighs 40 pounds and each 5 ft.³ box of clothing weighs 20 pounds. The commercial carries transporting food and clothing are bond by the following constraints: The total wave must be equal to 20,000 pounds. The total volume in cubic feet must equal to 8000 ft.³.

Answer 1

Let's define some variables.

F: number of cartons/boxes of food

C: number of cartons/boxes of clothing

W: total weight

V: total volume

Now we can write some equations.

W = 20,000 lbs

V = 8,000 ft³

F * (40 lbs) + C * (20 lbs) = W

F * (20 ft³) + C * (5 ft³) = V

This gives us the following simplified equations:

40F + 20C = 20,000

20F + 5C = 8,000

Footnotes:

1. I assumed "cartons" and "boxes" were the same things here, because I don't see information explaining the difference.
2. I assumed you meant "weight" instead of "wave".

Answer 2

Let's use the variables F and C:

F = the number of cartons of food

C = the number of cartons of clothing

Because each carton of food weighs 40 pounds and each box of clothing weighs 20 pounds, we can say:

40F = total weight of the cartons of food (40 times the number of food cartons)

20 C = total weight of the cartons of clothing (20 times the number of clothing cartons)

We also know the total between them must be 20,000 pounds. So we get our first equation:

40F + 20C = 20,000

Now we do the same for volume:

20F = total volume of cartons of food (20 square feet times the number of food cartons)

5C = total volume of cartons of clothing (5 square feet times the number of clothing cartons)

We also know the total volume between them must be 8000 square feet. Therefore:

20F + 5C = 8,000

So our system is:

40F + 20C = 20,000

20F + 5C = 8,000