Chapter Review Problems

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1 Chapter Review Problems Unit 4.1 Percent conversions Convert these decimals to percents =.079 = 7.9% = 1.35 = 135% Convert these percents to decimals % = 52.1% = % = 08.3% = % = 137.5% = % = % = Convert these fractions to percents =.875 = 87.5% = 1.25 = 125% Convert these percents to fractions % = % = % = 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 $ % of 250 = = $500 8% = $ = $40 = = % = = 87.5 Solve for base: = is 40% of what number? is 75% of what number? = = 40% 60 = = 150 = = 75% 240 = = 320 Check answer: % = 60 Check answer: % = 240 Solve for rate: = is what percent of 50? is what percent of 90? = = =.50 = 50% = = = 1.30 = 130% Check answer: 50 50% = 25 Check answer: % = 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, = $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) Percent correct Chapter Review Problems 81

2 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, = $25,620 Robbie: = = $42,700 40% = $42, = 17,080 $42, 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% = = 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? = = $ % = $ = $1.75 Check answer: $ % = $0.70 ($0.70) (40%) 22. You borrow $700 for 1 year at 9% interest. How much interest will you owe? = = $700 9% = $ = $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. = = $ % = $ = $85.71 Check answer: $ % = $ (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, = $160,000 Check answer: $160,000 15% = $24, 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, % 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: = = $ % = $ = $65.48 New amount: $970 (original amount) + $65.48 (increase) = $1, (15%) (3,450,000) (6,010,000) Percent down (100% - 85%) 82 Chapter 4 Percents

3 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% = $ = $26.16 New amount: $872 (original amount) - $26.16 (decrease) = $ 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: = = $ % = $ = $0.98 New hourly rate: $9.75 (original amount) + $0.98 (increase) = $ 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, , ,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 $ If approximately 35% of wages goes to federal and state taxes, what is your weekly gross pay? Net pay = = $ % = $ = $530 Check answer: $530-35%($530) = $ ($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 = sq ft 452 sq ft Check answer: %(451.76) = 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, % 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 $ % 34. During a year, the population for a small town decreased from 433 to 402. What is the percent decrease? = % 35. Your landlord raises your rent from $675 to $750. What is the percent increase? $750 - $675 $675 = $75 $ % Chapter Review Problems 83

4 36. During a 1-year period, the Dow Jones Industrial Average increased from 10, to 11, What is the percent increase? 11, , , = 1, , % 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, % 38. In the following news article is the information stated correctly? Explain your answer. 39. In the following ad, what is the percent discount? = % 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 $ $24.99 $45.95 = $45.95 $ % 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, = $16,450 Company share: $16,450 60% = $16, = $9,870 Your share: $9,870 70% = $9, = $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, = $5, 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, % 84 Chapter 4 Percents

5 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, % = $8, = $67, 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% Cost, including sales tax $58.85 Tip: $ % 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, % 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, % 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, % = $422, = $4,447, $4,447, In the chair ad, confirm that the reduced price is really 64% off. = $16.00 $ % $ $8.99 $ Refer to the newspaper article. Confirm the 17.88% decrease in net income. = % Chapter Review Problems 85

6 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. = = % 51. Write an essay answer to the Ask Marilyn question. Mr. Ely received only $ 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 % to a decimal number % = 87.5% = Convert 16 5 to a percent =.3125 = 31.25% 4. Convert 12.5% to a fraction. 12.5% = % = 25 2 % = = = 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, = $42, 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, % = $10, = $9,000 Check answer: $9, %($9,000) = $10,800 ($10,800) (120%) 86 Chapter 4 Percents

7 7. You take an exam with 24 questions and miss 3. What is your score, to the nearest tenth of a percent? Questions correct = = = 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% = $ = $52.50 New amount: $750 (original amount) + $52.50 (increase) = $ 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, = 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, % Practice Test 87

A Note to Students. and Practice Tests found in the 4 edition of the text. Here are a few suggestions for using these solutions:

A Note to Students. and Practice Tests found in the 4 edition of the text. Here are a few suggestions for using these solutions: A Note to Students Math skills are vital in business, investing, and everyday life as a consumer. Math for Business and Life was written to provide these math skills. The following pages include solutions