# Linear Systems

## Situation

An apartment manager is trying to find a magazine company that will deliver however many magazines the people in her apartments want. She is comparing two companies, Smith Inc. and Zines4lyfe . Smith Inc's cost includes a fixed cost of \$10 for delivery, along with \$3.50 per magazine included. Zines4lyfe's cost includes for a fixed cost of \$40, and only charges \$2 for each magazine.

## Utilizing Equations and Variables

As a lady that loves to impress her lessee's, she needs to decide which magazine company will be more satisfying for them but also efficient in cost. Now having it narrowed down to two companies, she is stumped. So she decides to make an equation of line for each company and compare them.

She decides to use the variables:

• C= total cost of the magazine

• m= number of magazines

Her equations for Smith inc. is-

C=3.50m+10

Her equation for Zines4lyfe is-

C=2m+40

## The Art of Comparing

The manager concluded that comparing the two equations isn't the best solution on comparing these two companies, so she makes a chart. In the chart, she included the total cost of each magazine using different values for her x variable (m).
Later on, she graphs this chart to have a better visual representation of her data.
She notices that the point of intersection for these two lines is (20, 80). Because the x variable is the number of magazines, 20 is the number of magazines that the lines will intercept at. The y variable is the total cost, the total cost is 80 for both equations when the number of magazines is 20.

## Conclusion

The manager concludes that the price depends on the number of magazines she needs. if she needs less than 20 magazines, she will subscribe to Smith inc. because it's more money efficient. But if she needs more than 20 magazines then she will subscribe to Zines4lyfe because they sell for less money than Smith inc.