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# Math Problems

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Part I. Basic Computations

1. A discount store sold plastic cups for \$3.25 each and ceramic cups for \$4.50 each.

a. If 500 cups were sold for a total of \$2,090, how many cups of each type were sold?
Answer:

b. What was the dollar value of each type of cup sold?
Answer:

2. LaToya Smith is a buyer for a large manufacturing company . She can purchase 200 pounds of chemicals for \$95. She can also purchase mixing vats for \$400 each. Sales tax on all products is 6% of the total cost of the order. Shipping costs for her order will be a flat \$30.

a. At this same rate, how much would 4,000 pounds of chemicals cost?
Answer:

b. This month she doesn't know yet how many mixing vats she will need to order. Let y = number of mixing vats required. Write an equation using y that she can use to determine the total amount of her order. Assume no chemicals are ordered, only vats.
Answer:

Part II. Case Study

3. Campus Painters offers house-painting services by hiring college students to paint during their breaks between semesters. John started the business when he was in college and now he owns and manages the small service-oriented business by providing price quotes, hiring student painters, purchasing supplies, and advertising their services. He currently employs 12 painters and pays them \$9.50 per hour for painting and "prep-work" (scraping old paint, caulking, cleaning and removing bugs from the areas that are to be painted).

In order to be profitable, John has learned to provide superior service to his customers, including free price quotes. He builds in his profit-margin of 25% to all quotes by first computing his total costs, then adding 25% of that number to determine how much to charge the customer. Using his knowledge of the expenses for labor, supplies, and equipment, he has developed the following information:

- 1 gallon of paint will cover approximately 400 square feet
- For every 2 gallons of paint for a wall, you need 1 gallon of paint for the trim
- John has a deal with the local paint store and can get any paint he wants for \$25 per gallon
[Note: John cannot purchase ½ a gallon of paint.]
- Every job requires 5 tubes of caulk (\$2.50 each) and 5 clean paint brushes (\$5 each).
- John finds that a painter can apply a gallon of paint in about 8 hours.

a. Martin just finished working on a job in which he spent 7 hours on Monday doing prep-work and 8.5 hours on Wednesday painting. How much money does John owe him?
Answer:

b. The Marks family needs to get the outside of their house painted, including the siding as well as the white trim. John estimates that area of the exterior of the house is about 6,000 square feet. Based on the condition of the Marks' house he also estimates that he will need 2 workers for 8 hours to do the prep-work. How much should John quote for the cost of this job, including labor, supplies, and profit?
Answer:

c. Write a formula reflecting the price estimate for a house based on the number of square feet that need to be painted. Assume that John can accurately estimate the painted area (in square feet) and the amount of time it takes to complete the prep-work on a job.
Answer:

d. What do you think? Using the evidence from above, explain in a well-structured essay the importance of accurate cost estimates in a service-oriented business such as this. Research at least one other service-oriented business such as a restaurant, dry-cleaners, house-cleaning service and describe how they set their prices. Be sure to describe the information that is used to prepare the estimate, using a real example.

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