zMath Intervention Math (19-36) - Unit 24: Applying Percent
Some of the questions in this unit may be answered by recording an audio file. If you chose to record the answer, click on the "Add Recording" button and follow the on-screen instructions closely. Once you have completed and attached the recording, enter the word “COMPLETE” in the text box. (Note: If your computer does not have a built-in microphone, a microphone or microphone/headset combination is needed to record audio.)

Sales Tax

1) Mindy purchased a computer for $899. How much sales tax did she pay if the tax rate was 7%?

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2) Sara bought a shirt for $19.99, jeans for $29.99, and a pair of shoes for $59.95. Sales tax on clothes is 6%. (a) What was the cost of the total purchase? (b) What was the sales tax on the purchase? (c) What was the final cost of the purchase? Round the answers to the nearest cent.

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3) Arlene purchased a desk set for $680. (a) How much sales tax did she pay if the tax rate is 6.5%? (b) What was the final cost of the desk set?

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Income Tax

Refer to the following scenario and the table below to solve the next four problems: Karen is single and earned a total of $85,968 in 2005. However, she was able to deduct $8,500 for job related expenses. This amount is to be subtracted from her total income to determine the taxable income.

4) What was Karen's taxable income in 2005?

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5) What was Karen’s base amount of income to be taxed? What was Karen’s “amount over” income to be taxed?

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6) What was Karen’s base tax? What was Karen’s tax on the “amount over”?

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7) How much income tax did Karen pay? Round the answer to the nearest dollar.

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8) The income tax is what percent of Karen's income (before deductions) for 2005? Round the answer to the nearest tenth of a percent.

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9) Larry sells used cars. He earns a 3.5% commission on sales for the month. His sales for one month were $52,500. What amount of commission did he receive for his monthly sales?

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10) Angie sells jewelry for a local jewelry store. She earns a 7% commission for her weekly sales. Last week, she sold $9,950 worth of jewelry. What was her commission for her sales for the week?

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11) Daniel earns a weekly salary of $300 plus 7% commission on sales over $5,000. If his sales for one week totaled $10,215, what was his total earnings for the week? Explain how to solve the problem.

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12) Jacob works for a computer store that pays 15% commission. What was the total of Jacob's monthly sales if he made $1,500 in commission for the month?

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13) Last month a real-estate agent received a commission of $8890 for selling a house for $122,850. What was her rate of commission?

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14) If the real-estate agent in the previous problem has a monthly salary of $1200 and sold only the one house, what was her total pay for the month?

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Discounts and Sale Prices

15) What is the discount and sale price of the sofa?

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16) What is the discount and sale price of the truck?

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Activity: Copy or print out (right-click / print) the table below. Find the sale price for each listed amount, and then fill in the Sale Price column. One method commonly used by many people is to compute the discount first, and then subtract to find the sale price. There is another way! Look over the completed Sale Price column. Try to devise another way to find the sale price by simply multiplying the original price by a percent that gives the sale price. (Hint: If an item is on sale for 10% off, then the sale price would be 90% of the original price.) Complete the second One-Step Percent Multiplier column. Refer to the completed table to answer the next three questions.

17) What is the sale price for each discount rate, a through e? State the letter, and then the amount.

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18) What is the one-step percent multiplier that will determine the sale price for each amount, f through k? State the letter, and then the amount.

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19) True or False. The sale price of an item can be determined by adding the discount rate to 100%, and then multiplying that percent times the original price.

20) What is the sale price of the boots? (Note: Try this problem using both methods discussed in the previous three problems. Use one method to calculate the answer and the other method to check the answer.)

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21) What is the discount rate for a stereo priced at $399.99, but on sale for 329.99? Round the discount rate to the nearest tenth of a percent. (Hint: First find the amount of discount.)

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22) Suppose the local department store paid $25 (wholesale price) for a pair of jeans from the manufacturer. The department store marked up (added) the cost of jeans by 30%. The jeans are priced at $32.50 (retail price) for the customers. Six months later, the department store placed the jeans on sale for 30% off. What is the sale price?

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23) Give a reason why the sale price of the jeans in the previous problem is not the same as the original wholesale price even though they were marked up 30%, then marked down 30%.

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Simple Interest

24) What is the simple interest on a loan of $5,500 at an annual rate of 5% for a time of three years?

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25) In the previous problem, what is the total amount that would be paid to the lending institution for the loan and interest?

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26) What is the interest earned on a deposit of $3000 at an annual rate of 6% for a length of 18 months?

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27) What is the simple interest on a loan of $22,000 at an annual rate of 7.75% for a time of 6 1/2 years?

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28) Mr. and Mrs. Smith paid a total interest of $72,000 for their house loan. The loan was at a rate of 4.5% for 20 years. How much was the principal on the loan? Use the substitution and algebra steps below to determine the answer.

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29) What was the total cost (loan + interest) of the home and loan discussed in the previous problem?

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Compound Interest

30) Calculate the savings total using compound interest for an account of $750 compounded semiannually for one year at a rate of 5.5%. (a) What was the total amount at the end of the first period? (b) What was the total amount at the end of the year?

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Print out (right-click / print) or copy the following chart as many times as needed to solve the next three problems.

31) Kim invested $2500 into a 1-year certificate of deposit at an annual interest rate of 2.7% and compounded quarterly. At the end of the year, she re-invested the new amount in a certificate of deposit at an annual interest rate of 4.3% and compounded quarterly. (a) What was the value of Kim’s investment after the first year? (b) What was the value of Kim’s investment after two years?

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32) Kelsey invested the same amount, $2500, in a 2-year certificate at 3.5% and compounded quarterly. What was the value of Kelsey’s investment after two years?

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33) Look over the investment plans of both Kim and Kelsey in the previous two problems. Which person made the better investment decision and why? No neutral responses will be accepted even though both girls increased their investments by about the same amounts.

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