Problem: 

 

Erin and Beth are on the Student Council Committee in charge of raising money for purchasing a sound system for the school.  The sound system costs $1,200.  They currently have $300 in the treasury.  To raise the money the committee thinks they can sell spirit items and baked goods every morning before school and at lunch which could net $75 per week.  They have exactly 12 weeks to raise the money.  Do they have enough time to raise the money?

 

Erin solves the problem

 

    

 

Beth solves the problem

300 + 75x

> 

1200

 

 

 

300 – 300 + 75x

> 

900 – 300

 

 

 

75x

                    75

> 

600

 75
     

x

> 

12 weeks

 

 

    

 

 

 

 

 

 

 

 

 

 

1200 – 75x

≤

300

 

 

 

1200 -1200 -75x

≤

300 - 1200

 

 

 

-75x

                   -75

≤

-900

 -75
     

x

≤

12 weeks

 

Erin reports that more than 12 weeks are needed.

 

    

 

Beth reports that at most 12 weeks are needed. 

It can be done!

 

1.   Are either of the inequalities set-up correctly to solve this problem? 

2.   If so, which? 

3.   Are they solved correctly?

4.   Who gives the correct recommendation?