**Should I Buy a Washer and Dryer?**

Gregory Graue

**Class:** Pre-algebra, middle school mathematics, or college-level developmental mathematics.

**Materials:** Calculator, appliance advertisements, and grocery store or department store advertisements.

**Goals:** This project will reinforce the concepts of simple interest and the total cost of purchasing and using an item weighed against the continuation of an alternative (e.g., renting). Estimation and critical thinking skills will be enhanced as students work to determine the total cost of buying and using a washer and dryer for five years or going to a laundromat for the same time period. The project will stress teamwork in problem-solving and presenting and explaining solutions to other students.

**Time Required:** One option is to introduce the project on Thursday, allow the students to gather information and formulate solutions on Friday, and have the group presentations the following Monday. You may wish to allow one week for the students to prepare written reports. For college students, after introducing the project in class, allow one weekend before the group presentations to the class. Allow one hour to explain the problem, assign project teams, and explain requirements for the written report and oral presentation and one hour for group presentations. You may wish to allow two weeks for the students to prepare a written report.

**Background:** Students need to know how to figure simple interest and perform cost calculations.

**Setting:** Often, a family faces a dilemma such as whether or not they can afford to purchase an item like a washer or dryer. Assume that you are married and have two children. You do not own a washer or dryer and have no money to pay cash for these appliances. You are weighing the possibility of borrowing the money necessary to buy a washer and dryer and wonder whether it would be cost efficient to do so.

**Problem:** Would it be cheaper to borrow money on an installment loan or continue going to the laundromat for the next five years? Assume the washer and dryer will be financed for the five years using simple interest. You will need to determine the number of loads of laundry a family of four will wash and dry over a period of five years.

**Note:** This simple interest assumption is not particularly valid, but one that will make the problem accessible to many students. Will this simplification of the problem allow for the same conclusion to be reached as would a loan with compound interest?

**Report Requirements:** Students will need to produce a list of assumptions indicating the interest rate used in financing the washer and dryer; the costs of water, gas, electricity, and soap; and the total number of loads of clothes washed and dried over the four years. Each assumption should be justified.

**Sample Solution:** A group of students concluded that a family of four does 10 loads of laundry each week. The cost of a trip to the laundromat was $2.75/trip. The family goes to the laundromat once a week. The total cost to wash and dry a load of clothes at the laundromat was $1.45.

__Calculations__:

Laundromat costs for five years:

10 loads/week X $1.45/load X 52 weeks/year X 5 years = $3,770.00

Laundromat transportation costs for five years:

$2.75/trip X 1 trip/week X 52 weeks/year X 5 years = $715.00

Total laundromat cost = $3,770 + $715 = $4,485

The students found the best purchase price of a washer and dryer to be $750.00. The students noted that Union Bank will finance the washer and dryer at 15% simple interest for five years.

Washer and Dryer costs for five years:

Interest = principal X rate X time

= $750 X 0.15 X 5 = $562.50

The students assumed 5% sales tax and a $25 delivery charge.

Sales tax = $750.00 X .05 = $37.50

By contacting local utility companies, it was discovered that it costs the average family of four $275/year for electricity and $85/year for water in the operation of a washer and dryer.

Total electricity costs = $275/year X 5 years = $1,375

Total water costs = $85/year X 5 years = $425

The students decided that a family of four uses two giant size boxes of laundry soap each month.

Total soap cost = 2 boxes/month X 12 months/year X 5 years = $418.80

Total washer and dryer cost =

$750 + $37.50 + $25 + $562.50 + $1,375 + $425 + $418.80 = $3,668.80

__Conclusion__: Upon comparing the cost of going to the laundromat and purchasing a washer and dryer, the family would be better off financially by purchasing the washer and dryer.

**Evaluation:** Give emphasis to the assumptions the students make to arrive at a mathematical conclusion in both the written report and group presentation. Require each student to speak at some point during the oral presentation to the class. For the written report, emphasize clarity of expression so that someone not in the class could read the report and understand the problem and the solution.

**Extensions:** This project can be extended to industrial applications in which a manufacturer needs to determine whether or not the company would be better off financially to keep a certain piece of equipment or purchase a new piece of equipment. Another compare/contrast problem is to examine the advantages and disadvantages of buying a car versus leasing one.

**Teacher Notes:** Students may shop for a washer and dryer using newspaper advertisements and determine the total costs of an installment loan using simple interest for five years. They should not forget sales tax, delivery charges, and the cost of soap! Also, they will need to determine the cost of gas, electricity, and water. For the laundromat, students will need to figure the cost of washing and drying a load of clothes and consider costs of driving to the laundromat.

Solutions should have a list of assumptions detailing how the costs of water, gas, electricity, soap, number of laundry loads, transportation, load at a laundromat, buying a washer and dryer, and the interest rate for financing the purchase of the washer and dryer were determined.

High school and junior high school students may have difficulty determining the costs of water, gas, electricity, laundromat, and transportation costs. A home economics teacher could be a handy resource for this modeling project and could possibly help you find information to give to students. Have the students estimate the number of loads of laundry a family of four will produce in a five year period in each group. Have the students in each group justify their conclusions based on assumptions.

You will need several appliance store and grocery store advertisements for this project. Each group of students must decide which washer and dryer to purchase. Have the students list the purchase price of the washer and dryer and why they decided to purchase that set of appliances. Do the same for the soap. You may need to find out or help the non-college students find an appropriate interest rate to use.

Students should be placed in groups of three or four with at least one high-achieving and one low-achieving student in each group.

**Should I Buy a Washer and Dryer?**

**Student Problem Sheet**

Group Members _______________________________________________________________

Setting: Assume that you are married and have two children. You do not own a washer or dryer and have no money to pay cash for these appliances. You are weighing the possibility of borrowing the money necessary to buy a washer and dryer and wonder whether it would be cost efficient to do so.

**Problem:** Would it be cheaper to borrow money on an installment loan or continue going to the laundromat for the next five years? Assume the washer and dryer will be financed for the five years using simple interest. You will need to determine the number of loads of laundry a family of four will wash and dry over a period of five years. Your parents may be able to assist you with this number.

You may shop for a washer and dryer using newspaper advertisements and determine the total costs of an installment loan using simple interest for five years. Don't forget sales tax, delivery charges, and the cost of soap! Also, you will need to determine the cost of gas, electricity, and water. For the laundromat, you will need to figure the cost of washing and drying a load of clothes and consider the cost of driving to the laundromat.

**Report Requirements:** You will need to produce a list of assumptions indicating the interest rate used in financing the washer and dryer; the costs of water, gas, electricity, and soap; and the total number of loads of clothes washed and dried over the five years. Each assumption should be justified.

*Funded in part by the National Science Foundation and Indiana University 1994*