Project Title

Painting Your Way to Profit

 

Introduction

There are numerous cases in which proportional reasoning helps to clarify thinking and illuminate the actual costs associated with doing business.

 

Task

In this project, your group will draft a plan for financing the start-up of your own painting company.  The owner of a local apartment complex is interested in hiring you to paint all of the apartments in his complex.  By using proportional thinking, your group will minimize costs, determine the terms of a contract with the owner of the apartment complex, and make a presentation to the bank from which you will seek a loan.

 

Instructions

Solve each problem in order and save your work as you progress, as you will create a professional presentation at the conclusion of the project.

 

1.      First problem:

 

·         Make a trip to the local paint store or, alternatively you can shop online at www.homedepot.com, which provides prices and specifications on paint products.  You will be painting inside, so select a single brand of interior paint.  Be sure that the paint is sold in quarts, gallons, and 5-gallon sizes.

 

·         Record the relevant information in the chart below. Use a proportion to determine the number of gallons in 1 quart, expressing your answer as a decimal. Note that there are 4 quarts in 1 gallon. In the table below, record all the volumes in gallons.

 

·         [Hint: To convert quarts to gallons, consider a proportion of the form  .]

 

·         Now compute the unit price of the paint. Be sure to justify the way in which you chose to compute the unit price and explain why it is the most relevant and informative.

 

[Hint:  When computing unit prices, there are two ways to compute them depending on whether you use the information on volume or coverage.]

 

 

Information on Paint Purchase Options

 

 

Option #1

quart container

Option #2

gallon container

Option #3

5-gallon container

 

Price

 

 

 

 

 

 

Volume

(in gallons)

 

 

 

 

Coverage

(in sq. ft.)

 

 

 

 

 

Unit Price

 

 

 

 

 


2.      Second problem:

 

·         You will now consider a simple scenario before attempting to calculate the cost of the paint needed for the entire apartment complex.  First, we will calculate the best purchase option for a wall that is 8 feet high and 12 feet long.  Make a sketch and determine the area of this wall (length x height).  From the information in your chart, determine whether to purchase paint in quarts (1, 2, or 3) or whether to purchase a gallon.

 

·         Based on your proportional thinking, you suspect that the coverage listed on the cans is not correct. You reason that since the amount of coverage depends on volume of paint in the can, the coverage amounts should be proportional.  Determine whether, for each option, the ratio of coverage to volume is the same.  If two of the ratios match and a third does not, determine the amount of coverage that would make the coverage rates proportional.  Does this new information change your decision to purchase paints in quarts (1, 2, or 3) or a gallon?

 

·          With your new coverage amount(s), re-compute your unit prices and record the new results in the table below.

 

 

Information on Paint Purchase Options

 

 

Option #1

quart container

Option #2

gallon container

Option #3

5-gallon container

 

Price

 

 

 

 

 

 

Volume

(in gallons)

 

 

 

 

Coverage

(in sq. ft.)

 

 

 

 

 

Unit Price

 

 

 

 

 

 

·         You decide to calculate the cost for various coverage areas using the unit prices.  Fill in the tables below using the unit prices you found in the preceding (revised) table.  Now determine the lowest cost for each coverage area.

 

 

Cost Using Quarts

 

Coverage Area

150 sq. ft.

500 sq. ft.

1500 sq. ft.

Cost using unit price

 

 

 

Number of quarts needed

 

 

 

Actual Cost of Paint Purchased

 

 

 

 

 

 

Cost Using Gallons

 

Coverage Area

150 sq. ft.

500 sq. ft.

1500 sq. ft.

Cost using unit price

 

 

 

Number of gallons needed

 

 

 

Actual Cost of Paint Purchased

 

 

 

 

 

Cost Using 5-Gallon Cans

 

Coverage Area

150 sq. ft.

500 sq. ft.

1500 sq. ft.

Cost using unit price

 

 

 

Number of 5-gallon cans

 

 

 

Actual Cost of Paint Purchased

 

 

 

 

 

 

 

 

 

·         You discover that unit cost is not the only consideration when calculating the cost of a job.  With this new information, your group needs to make a plan for purchasing paint. In the table below, there are various coverage areas.  For each, determine two different purchase options using combinations of quarts, gallons, and/or 5-gallon cans.  You should determine which option results in the least cost for each coverage area.  Remember to use the numbers from the Revised Information on Paint Purchase Options for your calculations.

 

Paint Purchase Plan

Coverage Area

(sq. ft.)

Purchase Option #1

(dollars)

Purchase Option #2

(dollars)

Least Cost

(dollars)

150 sq. ft.

 

 

 

250 sq. ft.

 

 

 

500 sq. ft.

 

 

 

800 sq. ft.

 

 

 

1500 sq. ft.

 

 

 

 

 

 

3.      Third Problem:

 

·         Next, your group will determine the cost of painting walls in one apartment in the complex. They are studio apartments (one large room) that are 33 feet by 15 feet and have 8-foot high walls.  So, there are two walls that are 33 feet by 8 feet and two walls that are 15 feet by 8 feet.  Make a sketch of each wall and calculate its area.

           

·         Based on your group’s previous plan, determine the best paint purchase option for this apartment. Calculate the actual cost of painting one apartment. Your group should make sure that your plan produces the lowest priced option for purchasing paint. Remember to use the numbers from the Revised Information on Paint Purchase Options for your calculations.

 

4.      Fourth problem:

 

·         Your group will estimate the cost of painting 3 apartments in the complex.  Adjusting your plan from Problem 2 above, determine the least cost for paint needed.

 

·         Next, determine the amount of labor needed for the job. Your group will assume four people can paint three apartments per eight-hour day and that you are paying each of them $10 per hour. 

 

·         Therefore, based on your paint price and cost for labor, compute the total amount your group would charge the owner for the three-apartment job.

 

·         Finally, your group will estimate the cost of painting the entire apartment complex, which contains 174 studio apartments. You will use this information to determine the terms of your agreement with the owner and make a presentation to a bank for a start-up loan for your painting company.

 

[Hint: You may want to use a proportion for this problem, such as .]

 

·         Your group will need to purchase paint up front to begin the job – before you receive any payment from the owner.  You plan to ask the bank for a $1,000 start-up loan.  Determine the number of apartments you could paint with that start-up money, before you would need to ask the owner for a partial payment, which you would then use to purchase more paint.

 

[Hint: You may want to use a proportion for this problem, such as ]

 

Collaboration

Get together with another group to compare your answers to each of the four problems.  Discuss how your group decided to purchase paint and explain your plan. Some groups may have chosen to go with extra paint, while some may have chosen to purchase exactly the paint they needed.

·        What if you were able to obtain a profit from painting an apartment?  What would be a reasonable amount to charge per apartment?

·        Would that change how many apartments you are able to complete with your start-up money?

·        What elements are missing from the plan?

·        Do some Internet research to determine how much extra you may need for miscellaneous items. Include your extras in the final presentation.

 

Conclusions

Your final presentation will be a professional analysis and report of the job to present to the bank in order to make your case in applying for the start-up loan. It should be in a binder or folder that will be presented to a bank. It should include all of the mathematics used to solve the four problems above.  You may either neatly write out the tables and draw the studio apartment or use software such as Microsoft Word to create a professional computer-generated product.  You may want to use headings to separate your plan into two parts: Labor and Materials.


 

Grade

Your presentation will be given a score of 1 to 4, with 4 being the highest score possible. You will be evaluated based on the following criteria:

 

Score

Content

Presentation

4

Your project appropriately answers each of the problems.  Your proportions are set up properly.  The step-by-step solution to each problem is given. 

 

Your project correctly identifies the total cost for painting the complex, how many apartments can be completed with the start-up money, and justifies the decision mathematically.

Your project contains information presented in a logical and interesting sequence that is easy to follow.

 

Your project is professional looking with graphics and effective use of color. 

 

3

Your project answers each of the problems.  Your proportions are set up and step-by-step solutions are given.  Minor errors may be noted. 

 

Your project identifies the total cost for painting the complex, how many apartments can be completed with the start-up money, and justifies the decision mathematically. Minor errors may be noted.

Your project contains information presented in a logical sequence that is easy to follow.

 

Your project is neat with graphics and effective use of color. 

 

2

Your project attempts to answer each of the problems. Proportions are attempted and solutions are given.  Major errors are noted. 

 

Your project attempts to identify the total cost for painting the complex, how many apartments can be completed with the start-up money, and justifies the decision mathematically. Major errors are noted.

Your project is hard to follow because the material is presented in a manner that jumps around between unconnected topics.

 

Your project contains low quality graphics and colors that do not add interest to the project.

1

Your project attempts to answer some of the problems.  Some proportions are attempted and solutions are given; however, little to no work is shown.  Major errors are noted.

 

Your project attempts to identify the total cost for painting the complex, how many apartments can be completed with the start-up money, but does not justify the decision mathematically. Major errors are noted.

Your project is difficult to understand because there is no sequence of information.

 

Your project is missing graphics and uses little to no color.


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