# Spending Low on Flooring

## Introduction

Bob's Flooring Inc. and Joe's Flooring Ltd. are often compared as the best and most popular flooring companies. Many people can have trouble deciding which company to hire, while considering the cost. This flyer will use linear equations and graphical solutions to determine which flooring company is the best to go with, specifically when looking to purchase hardwood flooring.

## Comparing Costs

Bob's Flooring Inc. charges a \$150 service fee plus an additional \$8 per square foot of hardwood. Meanwhile, Joe's Flooring Ltd. charges a \$450 service fee plus an additional \$5 per square foot of hardwood. Although Joe's Flooring Ltd. charges a much larger service fee than Bob's Flooring Inc., the cost per square foot is almost half of how much Bob's Flooring Inc. charges. Here is a table of values along with equations to compare the costs of both companies where "C" is the total cost and "n" is the number of square feet of hardwood being purchased.

## Graphing the Data

Here is a link to a graph comparing both flooring companies, as well as a screenshot of the graph, indicating the point of intersection. The pink line represents Bob's Flooring Inc. and the black line represents Joe's Flooring Ltd.

Link to graph - https://www.desmos.com/calculator/tqaewmpetq

Here is the exact point of intersection:

The equation of the pink line (Bob's Flooring Inc.) is y = 8x + 150. The equation of the black line ( Joe's Flooring Ltd.) is y = 5x + 450. As you can see, the lines intersect at (100, 950). This means that when the number of square feet of hardwood is 100, both companies will charge the same amount, \$950. This can be verified by solving by substitution.

We have two equations:

1. y = 8x + 150

2. y = 5x + 450

Equation 1 tells us that y is equal to 8x + 150, therefore, we can substitute what y is equal to into the second equation to solve for the x variable:

8x + 150 = 5x + 450

3x + 150 = 450

3x = 300

x = 100

We can then substitute x into one of the equations to solve for the y variable:

y = 8(100) + 150

y = 800 + 150

y = 950

Therefore, the point of intersection (x, y) is (100, 950).

## Which Flooring Company should you choose? When should you choose one over the other?

When deciding between two companies with different pricing, it is very important to understand the linear system and to come to a conclusion that will aid you in being financially responsible. Considering that the point of intersection is (100, 950), Bob's Flooring Inc. and Joe's Flooring Ltd. will both cost \$950 for 100 square feet of hardwood flooring. Despite the fact that Bob's Flooring Inc. has a service fee \$300 less than Joe's Flooring Ltd., Bob's Flooring charges almost double the cost per square foot than Joe's Flooring does and therefore causes its line on graph to intersect and pass the line of Joe's Flooring Ltd., even though Joe's Flooring Ltd's line had a y-intercept of 450, starting 300 above Bob's Flooring Inc. When considering cost, Bob's Flooring Inc. is the cheaper option if you are looking for 0-99 square feet of hardwood. At the 100 square foot mark, either company will do because they will charge the same amount of money. Lastly, Joe's Flooring Ltd. will be the cheaper option for any purchase of 101+ square feet. Overall, Joe's Flooring Ltd. would be the more popular choice as most families looking to renovate their floors would most likely be replacing or adding more than 100 square feet.