# Spirit Wear for Turner Fenton S.S

### Which clothing provider is the right choice?

## Deciding between Clothing Providers

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?

## Identifying and Illustrating Linear Equations

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

**form which is used to effectively portray the**

*y=mx+b***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

## -Graphing Costs

## Calculating and Recognizing the Point of Intersection

**(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

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.*

**Shreyas Krishna Prasad**

MPM-1D8

*Dec 12th, 2014*