Chapter Review Problems Unit 4.1 Percent conversions Convert these decimals to percents. 1..079 =.079 = 7.9% 2. 1.35 = 1.35 = 135% Convert these percents to decimals. 3. 52.1% = 52.1% =.521 4. 8.3% = 08.3% =.083 5. 137 1 2 % = 137.5% = 1.375 6. 5 8 % = 00.625% =.00625 Convert these fractions to percents. 7. 7 8 =.875 = 87.5% 8. 11 4 = 1.25 = 125% Convert these percents to fractions. 9. 36% = 36 100 1 100 36 25 9 10. 62.5% = 62 1 2 % = 125 2 100 1 200 125 8 5 For all remaining problems, if the answer is a percent, round to the nearest tenth of a percent. Unit 4.2 The percent formulas Solve for portion: = 11. 8% of $500 12. 35% of 250 = = $500 8% = $500.08 = $40 = = 250 35% = 250.35 = 87.5 Solve for base: = 13. 60 is 40% of what number? 14. 240 is 75% of what number? = = 40% 60 =.40 60 = 150 = = 75% 240 = 240.75 = 320 Check answer: 150 40% = 60 Check answer: 320 75% = 240 Solve for rate: = 15. 25 is what percent of 50? 16. 117 is what percent of 90? = = 25 50 =.50 = 50% = = 117 90 = 1.30 = 130% Check answer: 50 50% = 25 Check answer: 90 130% = 117 17. You, as a real estate agent, sell a property for $230,000. If you earn a 5% commission, what is your commission? = = $230,000 5% = $230,000.05 = $11,500? ($230,000) 18. You take an exam with 18 questions and miss 2. What is your score as a percent? (5%) Questions correct You get 16 correct, so: = = 16 18.889 88.9% (16) (18) Percent correct Chapter Review Problems 81
19. Matt and Robbie are partners in a restaurant. Matt is to receive 60% of the profits and Robbie is to receive the remainder. If this year s profits were $42,700, how much should each receive? Matt: = = $42,700 60% = $42,700.60 = $25,620 Robbie: = = $42,700 40% = $42,700.40 = 17,080 $42,700 20. A B grade on a certain test is 85%. How many questions can you miss on a 35-question exam to get a B? Questions you must answer correctly: = = 35 85% = 35.85 = 29.75 Because it is not possible to get.75 of a question correct, you must get at least 30 questions correct to get at least 85%. This means you can miss no more than 5 questions to get a B. 21. You own a small restaurant. You are trying to determine what price you should charge for your meals. If ingredient costs should be 40% of the retail price of the meal and the ingredients for a grilled cheese sandwich cost 70, what should you charge customers for a grilled cheese sandwich? = = $0.70 40% = $0.70.40 = $1.75 Check answer: $1.75 40% = $0.70 ($0.70) (40%) 22. You borrow $700 for 1 year at 9% interest. How much interest will you owe? = = $700 9% = $700.09 = $63 ($700) (9%) 23. Joe, an antiques dealer, is thinking about buying a 60-year-old rocking chair. He customarily sells antiques for 350% of cost. What price should Joe pay for the rocking chair if he thinks it will sell for $300. = = $300 350% = $300 3.50 = $85.71 Check answer: $85.71 350% = $299.99 (penny difference due to rounding cost to exactly $85.71) ($300) (350%) 24. You want to buy a home. You can borrow 85% of the purchase price. Assuming you can make a down payment of $24,000, what price home can you afford? Down payment ($24,000) = = $24,000 15% = $24,000.15 = $160,000 Check answer: $160,000 15% = $24,000 25. The population of the largest county in a state is 3,450,000, while the population for the entire state is 6,010,000. What percent of the state s population resides in the largest county? = = 3,450,000 6,010,000.574 57.4% Unit 4.3 Increase and decrease problems 26. You are about to buy a refrigerator priced at $970. You must pay 6.75% sales tax. First, find the dollar amount of sales tax. Then, find the total amount you must pay including sales tax. Sales tax: = = $970 6.75% = $975.0675 = $65.48 New amount: $970 (original amount) + $65.48 (increase) = $1,035.48 (15%) (3,450,000) (6,010,000) Percent down (100% - 85%) 82 Chapter 4 Percents
27. A local utility company declares that utility rates for this year will be 3% less than last year s rates. If your utility costs were $872 last year, what can you expect to pay this year? : = = $872 3% = $872.03 = $26.16 New amount: $872 (original amount) - $26.16 (decrease) = $845.84 28. Your boss promises you a 10% pay raise in 2 months. If you currently earn $9.75 an hour, what will your hourly rate be in 2 months? Pay raise: = = $9.75 10% = $9.75.10 = $0.98 New hourly rate: $9.75 (original amount) + $0.98 (increase) = $10.73 29. A customer orders 75,000 car batteries. If experience has shown that 8% of batteries produced will be defective, how many batteries must be produced to ensure production of 75,000 good ones? Good ones = = 75,000 92% = 75,000.92 81,521.74 81,522 batteries Note:.74 of a battery is not much good, so we round up to 81,522. Check answer: 81,522-8%(81,522) 75,000 (75,000) (92%) for good ones (100% - 8%) 30. You receive your weekly paycheck in the amount of $344.50. If approximately 35% of wages goes to federal and state taxes, what is your weekly gross pay? Net pay = = $344.50 65% = $344.50.65 = $530 Check answer: $530-35%($530) = $344.50 ($344.50) (65%) 31. What amount of wallpaper should you purchase if you need to cover 384 square feet of wall area and 15% of the material purchased will be wasted? Round to the nearest square foot. Good stuff = = 85% 384 = 384.85 451.76 sq ft 452 sq ft Check answer: 451.76-15%(451.76) = 384.00 32. The population of a town increased from 13,577 last year to 14,817 this year. What is the percent increase? (384) (85%) for net pay (100% - 35%) for good stuff (100% - 15%) 14,817-13,577 13,577 = 1,240 13,577.091 9.1% 33. A year ago, your uncle purchased a set of golf clubs for $429. You want to buy the same set but the retailer s price has increased to $479. What is the percent increase? $479 - $429 $429 = $50 $429.117 11.7% 34. During a year, the population for a small town decreased from 433 to 402. What is the percent decrease? 433-402 433 = 31 433.072 7.2% 35. Your landlord raises your rent from $675 to $750. What is the percent increase? $750 - $675 $675 = $75 $675.111 11.1% Chapter Review Problems 83
36. During a 1-year period, the Dow Jones Industrial Average increased from 10,242.53 to 11,844.22. What is the percent increase? 11,844.22-10,242.53 10,242.53 = 1,601.69 10,242.53.156 15.6% 37. If your gross pay is $2,200 per month and your take-home pay is $1,477, what percent of your gross pay is withheld? $2,200 - $1,477 $2,200 = $723 $2,200.329 32.9% 38. In the following news article is the information stated correctly? Explain your answer. 39. In the following ad, what is the percent discount? 43.5-31.9 31.9 = 11.6 31.9.364 36.4% The article is incorrect. Loan volume has increased 36.4% not 26.7%. Whoever prepared the article made a mistake by dividing the increase ($11.6 million) by the new amount ($43.5 million). Challenge problems $45.95 - $24.99 $45.95 = $45.95 $20.96.456 45.6% 40. You are a real estate agent with ABC Real Estate Company. You help sell a home for $235,000. The total commission is 7%. Your company is to receive 60% of the total commission; you will receive 70% of that amount. What is your personal share of the commission? Total commission: $235,000 7% = $235,000.07 = $16,450 Company share: $16,450 60% = $16,450.60 = $9,870 Your share: $9,870 70% = $9,870.70 = $6,909 For Problems 41 43, answer questions about a Keogh retirement plan. 41. You, as the owner of a small business, have a Keogh retirement plan. Suppose your plan allows annual contributions up to 13% of net income (profit). If your net income was $42,378, what is your maximum allowable contribution? = = $42,378 13% = $42,378.13 = $5,509.14 42. If, for a particular year, you made a contribution of $2,000 and had net income of $28,000, what percent contribution was made? = = $2,000 $28,000.071 7.1% 84 Chapter 4 Percents
43. You cannot remember what your net income was 5 years ago, but you know you made a maximum allowable contribution to your Keogh plan. If your contribution was $8,718.45, what must your net income have been? = = $8,718.45 13% = $8,718.45.13 = $67,065 44. You and your dining partner are thinking about ordering the romantic dinner for two costing $55. If the sales tax rate is 7% and you want to leave a 15% tip (based on the total cost of the meal, including sales tax), should you order the $55 meal if you have only $65? Cost of meal $55.00 Sales tax: $55 7% + 3.85 Cost, including sales tax $58.85 Tip: $58.85 15% + 8.83 Total cost $67.68 No, the total cost is more than you have. For Problems 45 and 46, answer questions about a fund-raising campaign. 45. A local charity has a goal of raising $3 million. If $1,895,218 has been raised 3 weeks before the end of the campaign, what percent of the goal is reached? = = $1,895,218 $3,000,000.632 63.2% 46. If at the end of the fund-raising drive $3,340,865 is raised, what percent of the goal has been reached? = = $3,340,865 $3,000,000 1.114 111.4% 47. The annual net income on a neighborhood shopping center is $422,500. Richard Martinez is interested in buying the property and wants to earn 9.5% on his investment. What price, rounded to the nearest thousand dollars, should he pay for the property? = = $422,500 9.5% = $422,500.095 = $4,447,368.42 $4,447,000 48. In the chair ad, confirm that the reduced price is really 64% off. = $16.00 $24.99.640 64% $24.99 - $8.99 $24.99 49. Refer to the newspaper article. Confirm the 17.88% decrease in net income. = 12.3 68.8 68.8-56.5 68.8.1788 17.88% Chapter Review Problems 85
50. In the news report, precipitation through October 1 is 7.33 inches, while the normal is 8.85 inches. Confirm that this year s precipitation is actually 83% of normal. = = 7.33 8.85.83 83% 51. Write an essay answer to the Ask Marilyn question. Mr. Ely received only $650.50 back from his original $1,000 investment! This happened because Volatile always increased from lower prices and dropped 20% from higher prices. For example, on the first day, the stock value increased 20%, turning it into $1,200. But on the second day, the value decreased $240 (20% $1,200), turning it into only $960. Then the cycle kept repeating, sending the price lower and lower. Practice Test 1. Convert.065 to a percent..065 =.065 = 6.5% 2. Convert 87 1 2 % to a decimal number. 871 2 % = 87.5% =.875 3. Convert 16 5 to a percent. 5 16 =.3125 = 31.25% 4. Convert 12.5% to a fraction. 12.5% = 12 1 2 % = 25 2 % = 25 2 100 1 = 200 25 = 1 8 5. If you buy a home for $210,000 and need 20% for a down payment, what is the dollar amount of the down payment? = = $210,000 20% = $210,000.20 = $42,000 6. Ed, a used car dealer, is thinking about buying a 3-year-old vehicle. He customarily sells the cars for 120% of his cost. What price should Ed pay for the car if he thinks he can resell it for $10,800? = = $10,800 120% = $10,800 1.20 = $9,000 Check answer: $9,000 + 20%($9,000) = $10,800 ($10,800) (120%) 86 Chapter 4 Percents
7. You take an exam with 24 questions and miss 3. What is your score, to the nearest tenth of a percent? Questions correct = = 24 21.875 = 87.5% (24) (21) Percent correct 8. You buy a TV for $750. You must also pay sales tax of 7%. What is the total amount you must pay? Sales tax : = = $750 7% = $750.07 = $52.50 New amount: $750 (original amount) + $52.50 (increase) = $802.50 9. A customer orders 21,000 tires. If experience has shown that 4% of tires produced will be defective, how many tires must be produced to ensure production of 21,000 good ones? Good ones = = 21,000 96% = 21,000.96 = 21,875 tires Check answer: 21,875-4%(21,875) = 21,000 (21,000) (96%) Percent good (100% - 4%) 10. The population of a town decreased from 8,422 to 8,318. What is the percent decrease, to the nearest tenth of a percent? 8,422-8,318 8,422 = 8,422 104.012 1.2% Practice Test 87