System of equations

Question

A farm has 200 acres available to plant cabbage, watermelons, and beans. An acre of cabbage requires 5 hours of labor, watermelon 6, beans 4. There are 1000 hours of labor available. 

 

1.Set up a system of equations that describes the data. 

 

2.If the farm decides to plant 50 acres of cabbage, how much will be planted in beans and watermelon? 

 

3.If the farm plants 80 acres of beans, how much will be planted in cabbage and watermelon?

Answer 1

Let c=acres of cabbage, w=acres of watermelon, b=acres of beans.

 

The system of equations is:

c + w + b = 200 acres         

5c + 6w + 4b = 1000 labor hours

 

If c=50 acres:

50 + w + b = 200 acres

Subtract 50 from both sides:

w + b = 150 acres

 

If b=80 acres:

c + w + 80 = 200

Subtract 80 from both sides:

c + w = 120 acres