SOLUTION: You are the SSG President of your school. In the incoming foundation anniversary of your school, the SSG team agreed to have printed t-shirt in all grade level. You have two printi

Question 1161813: You are the SSG President of your school. In the incoming foundation anniversary of your school, the SSG team agreed to have printed t-shirt in all grade level. You have two printing services available in your town. You want to help your teachers decide on what printing services to choose. One printing services charges Php 50.00 per shirt with free setup fee. Another printing services charges Php 45.00 per shirt but with a set up fee of Php 250.00.
1. Which system of linear equation will you use to find how many shirts would have the same cost to both printing services?
2. Which method of solving systems of linear equations will help you easily in finding reasons which printing services to choose?
3. Below are the number of students per grade level
Grade 7 : 56 students
Grade 8 : 50 students
Grade 9 : 48 students
Grade 10: 52 students
In what printing services will you choose? Why?

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Informally....

The difference in cost per shirt is Php 5; the difference in the setup fee is Php 250. The number of shirts to make up the difference in setup fee is 250/5 = 50.

So the price will be the same if 50 shirts are printed.

That means if the number of shirts is greater than 50 the service with the lower cost per shirt should be used; if the number is less than 50, the service with no setup fee should be used.

Assuming a separate order for the different grades is to be made, it is clear that one service should be used for some grades and the other service for other grades -- and that the cost for the shirts for grade 8 will be the same with either service.

Formally....

1.

2. Use substitution. You want to find when the cost of the two services is the same; the two equations show different expressions that are both equal to y. So write the equation that says those two expressions are equal:

3. Solve the equation from 2. to find the number of shirts x that makes the cost the same for both services.

Then use the service with the lower cost per shirt if the number of students in a grade is more than x, or use the service with no setup fee if the number of students is less than x.

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