# Spirit Wear for Turner Fenton S.S

## Deciding between Clothing Providers

Duncan, a student from Turner Fenton Secondary School is the executive partner of the schools student council. Duncan has been assigned the responsibility of selecting a clothing supplier to provide a specific fabric material for this years spirit wear accessories. He has to decide between two services, Brandi’s Outfitting and Samson’s Attire which provide clothing material at different prices.

Brandi’s Outfitting offers clothing services at a fixed price of \$20 and \$4 for every additional foot of material while Samson’s Attire offers clothing at \$8 per foot. In which conditions would Duncan advise the council to pick one service over another?

## -Applying y=mx+b (equation of a line)

Both prices the two clothing material provide can be written in the y=mx+b form which is used to effectively portray the constant value (initial cost) and constant multiple (cost per foot of material). As shown in the image to the left, the line formulas can be interpreted from the text that corresponds to their values. Duncan realizes these respective line formulas can then be used to determine a table of values and a graph which can be used to identify which service is the ideal choice for Turner Fenton under certain circumstances.The total cost values of any amount of clothing material can be calculated simply by applying a value of 'x' (amount of clothing material) in the respective line equation to find 'y' (total cost).

## -Comparing Cost with a Table of Values

The following table of values compares the total prices for both clothing services at different amounts of clothing material.

## -Graphing Costs

The graph shown below is a visual representation of the total prices offered by the two clothing services at different amounts of clothing material.

## Calculating and Recognizing the Point of Intersection

Duncan deduces that the point of intersection in this case is the point where both services have the same total cost for the same amount of clothing material. As expressed in the graph and table above the point of intersection is (5,40) which means both services have a total cost of \$40 for 5 feet of clothing material even though they have different prices and rates.

Duncan's best friend, Ray, demonstrates that this value can also be determined in an equation format where the 'x' value of the point of intersection is found and then applied to calculate the 'y' value. This process is shown below.

## Significance of this Linear System in a Real Life Context

Using the knowledge that Duncan has acquired about this linear system such as it's point of intersection and line equations, he can effectively relate this information to the real life situation he was initially presented with.

Based on the amount of clothing the school requires, Duncan would consider which service to use based on the cost of each service at particular amounts of clothing material.

## Summary Statement

Both clothing services cost \$40 for 5 feet of material. If the school required an amount of clothing material below the mark of 5 feet, Duncan would recommend they choose Samson's Attire which would offer the same amount of clothing material as Brandi's Outfitting, but at a lower price. However, if the school required more than 5 feet of clothing, Duncan would suggest that they choose Brandi's Outfitting which would offer lower prices than Samson's Attire at any point above 5 feet of material.The amount of clothing material required would depend entirely on the general demand for spirit wear. Using this information, the school would purchase accordingly. Lastly, considerations that Duncan would make other than the price of the service would include quality of material, convenience of access, availability of colours, and the service's reputation.

Examining all these factors and the mathematical reasoning behind this linear system would assist Duncan in making the best possible decision when advising the council to pick a

clothing service to employ.