Open ended question

Question

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Food and clothing are shipped to victims of a natural disaster. Each 20​-cubic-foot box of food weighs 40 pounds and each 5​-cubic-foot box of clothing weighs 20 pounds.

 

The commercial carriers transporting food and clothing are bound by the following​ constraints:

​- The total volume in cubic feet must equal to 8,000 cubic feet.

​- The total weight must be equal to 22,000 pounds.

 

 

1. Write a System of Equations using the information given

 

2. Solve the system of equations you have written

 

3. Identify the number of food cartons needed.

 

4. Identify the number of clothing cartons needed.

Answer 1

x = the number of food cartoons

y = the number of clothing cartoons

1: 40x + 20y = 22000 (total weight in pounds)

2: 20x + 5y = 8000 (total volume in cubic feet)

Multiply the 2nd equation by -2 on both sides to start the elimination method.

40x + 20y = 22000

-40x - 10y = -16000

Add up the equations from above, then divide both sides by 10 and you get

10y = 6000 → y = 600

Plug in the 600 for y in one of the original equations to find x. Therefore, you get

20x + 5(600) = 8000

20x + 3000 = 8000

20x = 5000

x = 250

Let's go ahead and check our solutions.

40(250) + 20(600) = 10000 + 12000 = 22000

20(250) + 5(600) = 5000 + 3000 = 8000

The commercial carriers will need to transport 250 food cartoons and 600 clothing cartoons.

Answer 2

Let x be food box which weights 40 pounds and volume 20 cubic feet

Let y be clothing box which weights 20 pounds and volume 5 cubic feet

The total volume in cubic feet must equal to 8,000 cubic feet means 20x+5y=8000

The total weight must be equal to 22,000 pounds means 40x+20y=22000

Your system of equation is

20x+5y=8000

40x+20y=22000

Before you solve this system, you can simplify it by dividing first equation by 5 and second equation by 20

4x+y=1600

2x+y=1100

You should be able to solve this system of equation and find the answer to questions 3 and 4