The Box Method There are different methods for solving problems involving percents. An easy and dependable method is The Box Method. When you can analyze which number is missing from the problem, then you can set up a proportion in a box and easily find the number you need. part % whole 100 Step 1 Step 4 Decide whether you are looking for the part, whole, or percent. Fill in the box with the information you have. Multiply the numbers on the diagonal which has two numbers. Divide the answer (product) in Step 3 by the number on the other diagonal, and put the answer (quotient) in the empty box. Rose is a new agent with Royal Realty. She sold her first condominium on Saturday. She got a 6% commission on the sale and just received her check for $8,700.00. What was the sale price of the condo? 1. The numbers you have are 6 and $8,700.00. Six is the percent and 8,700.00 is the part of the sale that Rose received as her commission. You are looking for the whole, the selling price of the condo. 2. 8700 6 whole 100 3. 8,700 x 100 = 870,000 4. 870,000 6 = 145,000 The sale price of the condo was $145,000.00. 1
Analyze the question to find the missing element and then use the box method to find the answers to the following problems. Use the boxes below for your work space. Find 15 % of 60. 27 is what % of 45? 72 is 45% of. 30 % of is 21 22 is % of 176 48 is % of 64 192 is 60% of 35 is % of 56 45% of 80 is 2
125% of 64 = 21 is % of 140 24 is % of 60 87% of 400 = 20% of 40 = 80 is % of 20 Now solve these problems. Remember sometimes another step is needed to get to the final answer. Read the question carefully. A dress originally selling for $40.00 was on sale for 15% off. How much did the dress cost if it was purchased on sale? Mr. And Mrs. Chao need $8,000 for a down payment on a house. So far they have saved $6,000. What percent of the total amount do they still need to save? Jamal is in training for football season. A year ago he weighed 178 pounds. He took off some weight hoping to gain speed as a running back. He lost about 5% of his body weight. About how much does Jamal weigh now? Alice makes $600 a month at her job at Tasty Taco. She puts $150.00 into savings each month for her college fund. What percent does she save each month? Tasty Taco Eighteen adult students came to Ms. Towne s algebra class. This was 75% of the students registered for the class. How many people are registered for the class? 3
The Box Method is a good way to solve problems about percents. Here is a summary of the advantages: You can learn to identify which piece of information is missing and correctly place the two pieces of information that are given into the boxes. The same method is used for all types of problems; there is no need to learn three separate sets of rules. The Box Method is quick and easy. No movement of the decimal point is necessary. There are also some cautions to using The Box Method: Do not confuse this method with multiplication of fractions. You cannot cross cancel. Either column may be treated as a fraction and can be reduced. Modifications are needed to solve for special situations, i.e. percent of increase and percent of decrease and using the formula for simple interest. Quick Review: Pppppppppaa Write the labels for each section of the box to practice that you are now able to set up the problems each time. Then write out the steps that you use to solve the problem each time. The method is always the same no matter which box is empty. Step 1 Step 4 Now you are ready to learn how to modify the box for special situations such as percent of increase, percent of decrease, and finding simple interest. Brewer/Rogers Revised 11/06 4
Percent of Increase and Percent of Decrease You can modify the box to find percent of increase or percent of decrease. These problems are found on the GED Math Test. difference *Note that change may (change)* % go up or down as the percent can increase or decrease. original 100 After Mr. and Mrs. Andrews bought their new car for $24,000, they decided to sell it after three years. The value of the car was then listed as $19, 800. What was the percent of depreciation (lost value) of the car? Compute the difference or change in the original value and the new value. $24,000-19,800 = $4200.00 4200 x 100 = 420,000 420,000 = 17.5 4200 x 24,000 The car had depreciated 17.5% in three years. 24000 100 Use the modified box to find the answers to these problems about percent of increase or percent of decrease. Original Amount 1000 Original Amount 280 Original Amount $24.00 New Amount 1800 New Amount 70 New Amount $ 36.00 Juan was given a raise after he had been on the job for six months. His starting pay was $1200 a month. After the raise he made $1260 a month. What percent did his pay increase? The New Wave Cinema sold tickets for 7.50 when a show was new the theater. After a successful run, the management sometimes kept the show running and discounted the tickets $5.00. What was the percent of decrease in this type of ticket? 5
Interest The formula for finding simple interest is I = PRT. Interest = Principal x Rate x Time. Use the box to find missing number and then multiply the result by the time relative to one year. Mr. and Mrs. Andrews bought a new car for $24,000. They got a simple interest loan for 8% for two years. The part of the loan is the interest owed. The whole amount of the loan is the principal. The percent is the rate of 8%. part 8 24,000 100 192,000 = $1,920 Now multiply by 2 because the loan 100 two years. 1,920 x 2 = $3,840 is the total amount of interest that Mr. and Mrs. Andrews will pay. Try solving these problems to find the interest that will be earned or paid in each situation. I = PRT Interest = Principal x Rate x Time (relative to one year) You will see this formula on the Formula Page that is provided when you take the GED Math Test. Try these problems. Tanya s Uncle Joe said he would give her some money so she could start a savings account. He gave her $500.00. She opened an account with 3% interest. How much interest had the account earned after the first six months? If Tanya did not make any withdrawals, how much money was in her account at the end of the first eight months? the first year? the first year and a half? the second year? The Energy Efficient Engineers wanted to open a new business to design playground structures made from recycled materials. They were able to get a small business loan for $10,000 at 7% interest. They paid off the loan in 18 months? How much interest did they pay? 6
The new business, The Energy for Play, did very well in the first two years. The engineers wanted to concentrate on new product development. They had set aside money in a Certificate of Deposit for this purpose. They bought the certificate for $6,500. The certificate matured at the end of the year with 3.5% interest. How much money did the engineers have to develop the new product? Marlene had a savings account and prided herself on not using the principal. Each year she would withdraw the interest and spend it on a vacation. Her account had a principal of $15,250. It earned 2.8 percent interest. How much did she have to spend for the last three vacations combined? Mixed Review What are the entries for the four parts of the box when using The Box Method to solve problems with percents? To use the box correctly, you first have to analyze the section of the box is that is. Then you can follow the steps to solve the problem. What is 25% of 364? 34 is % of 680 55 is 40% of % of 300 is 125 125% of 400 is 10 =.5%(1/2%) of Approximately what is the percent of increase of the value of a vintage, wooden sailboat that was purchased for $15,500.00 and sold for $16,800 two years later? How much interest did Mercedes earn in a year on a savings account that earned 2.8% interest if she deposited $550.00 that she earned at summer camp? Now write your own word problem. Use The Box Method to solve the problem. 7
Answers and Explanations The Box Method page 2/3 part 15 percent 27 45 72 60 100 100 45 100 whole 9 60% 160 70 12.5% 75% 320 62.5% or 62 1/2% 36 80 15% 40% 348 8 400% The Box Method (Word Problems) page 3 $34.00 25% 169 pounds 25% 24 students Quick Review page 4 part % whole 100 Step 1 Step 4 Decide whether you are looking for the part, whole, or percent. Fill in the box with the information you have. Multiply the numbers on the diagonal which has two numbers. Divide the answer (product) in Step 3 by the number on the other diagonal, and put the answer (quotient) in the empty box. Percent of Increase and Percent of Decrease page 5 80% increase 75% decrease 50% increase 5% 33% 8
Interest page 6/7 $7.50 $510.00 $515.00 $522.50 $530.00 $1,050.00 $6,727.50 $1281.10 Mixed Review page 7 part, whole, %, 100 missing 91 5 137.5 41.67 % or 41 2/3% 500 2000 approximately 8% $15.40 Answers will vary. Share yours with a classmate, tutor, or teacher. 9