Use the information to create a system of equations

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

Hello, Jay,

The best I can do is are equations that tell the total volume and weight. There is not enough information to calculate the numbers of boxes of each that might make up a shipment.

The last 2 lines are the two equations. F = food cartons and C = clothes cartons.

But they need to be written as F*40 + C*20 < 20,000 pounds, and

F*20 + C*5 < 8,000 ft^3

Bob

Answer 2

First, you make an equation for the pounds. Since we know the total, we can write:

40 lbs*F + 20 lbs*C = 20000 lbs,

where F and C are the number of food and clothing boxes, respectively.

Next, we do the same thing for the size.

20 ft³*F + 5 ft³*C = 8000 ft³

Now, we have a system of 2 equations with two unknowns, which we can write in matrix form, if you prefer to solve the system of equations in this way:

(40 20 | 20,000 )

(20 5 | 8000 )