Three people invest in a business. The first two invest in the ratio 2:3, and the third person invests twice as much as the other two combined. The total invested is $30 million. a. How much did the major investor contribute? b. Does the major investor own more than half the business? c. What fraction of the business does the major investor own?
> Bernie bought a refrigerator at a special sale. The refrigerator regularly sold for $986. No down payment was required. Bernie has to pay $69 per month for 1½ years. What is the average amount Bernie pays in interest each month?
> Chris purchases living room furniture for $4,345 from Halloran Gallery. She has a 1-year, no-interest, no-money-down, deferred payment plan. She does have to make a $15 monthly payment for the first 11 months. a. What is the sum of these monthly paymen
> How might the quote apply to what you have learned?
> If Tanya purchased a $1,700 set of golf clubs on a 9-month layaway plan and had to pay a monthly payment of $201, what is the sum of the monthly payments? What was the fee charged for the layaway plan?
> Mary wants to go on a $10,000 vacation in 6 months. She has a bank account that pays 2.25% interest, compounded monthly. How much must she deposit each month to afford the vacation?
> Kate is a professional musician. She wants to make an essential purchase of an upgraded used bass guitar for her work. She found the following prices for the same make and model bass guitar from various sellers: $699, $599, $699, $680, $590, $720, $650,
> Adam bought a $1,670 custom video game/sound system on a special no-interest plan. He made a $100 down payment and agreed to pay the entire purchase off in 1½ years. The minimum monthly payment is $10. If he makes the minimum monthly payment up until the
> Interpret the quote in the context of what you learned about consumer credit in this section. Solve each problem. Round monetary amounts to the nearest cent.
> Nick and Liz have decided to move from the city to the suburbs. This means that they will have to make the essential purchase of a car in order to get to work. They researched used 2-year-old cars of the same make, model, condition, and equipped with the
> Medications are essential expenses. DeWitt has composed a price list of antibiotics available at different pharmacies in his neighborhood. In reviewing his list, he can’t find the number of pharmacies selling the antibiotics for $8. Examine the frequency
> The following arithmetic sequence models an installment purchase. Give the down payment, monthly payment, and length of the plan. 400, 510, 620, 730, 840, 950, 1,060.
> Samantha’s grandfather is debt-free—he bought his car and his house without taking out a loan. He saved and paid cash. He wanted to take out a loan to buy Samantha a car for college graduation. The bank turned him down. Explain why.
> The following inequalities give information on your credit scores. Let x represent your credit score. • If x > 700, your credit score is excellent. • If 680 < x < 700, your credit score is good. • If 620 < x < 680, your credit score should be watched car
> Write the sigma notation mean formula for the 4 consecutive days that would have the lowest mean of the week. Elizabeth wants to change cell phone plans. Before contacting the service provider, she makes a table of her cell phone minutes used over the co
> Darlene purchases $20,000 worth of stock on her broker’s advice and pays her broker a 1.5% broker fee. She sells her stock when it increases to $28,600 two years later, and uses a discount broker who charges $21 per trade. Compute Darlene’s net proceeds
> Omar wants to open an account for his grandchildren that he hopes will have $80,000 in it after 20 years. How much must he deposit now into an account that yields 1.75% interest, compounded monthly, so he can be assured of reaching his goal?
> The piecewise function describes a newspaper’s classified ad rates. a. If x represents the number of lines, and y represents the cost, translate the function into words. b. If the function is graphed, what are the coordinates of the
> Some stores offer a rent-to-own plan. The customer makes a down payment, receives the merchandise at time of purchase, and makes monthly payments. The sum of the monthly payments is lower than the cost of the item. When the last payment is made, customer
> Audrey purchases a riding lawnmower using a 2-year, no-interest deferred payment plan at Lawn Depot for x dollars. There was a down payment of d dollars and a monthly payment of m dollars. Express the amount of the last payment algebraically.
> Online Car Auctioneer charges a commission for classified ads. If the car sells, the seller is charged 4% of the advertised price, not of the price for which the car actually sells. If the car doesn’t sell, the seller pays nothing. If Barbara advertises
> Leslie placed this ad in Collector Car Monthly. a. If the publication charges $48 for the first three lines and $5 for each extra line, how much will this ad cost Leslie? b. Ruth buys the car for 8% less than the advertised price. How much does she pa
> The Good Ole Times magazine charges for ads by the “column inch.” A column inch is as wide as one column, and it is 1 inch high. The cost is $67 per column inch. How much would the magazine charge to print a 2½-inch ad?
> The Kings Park Register gives senior citizens a 10% discount on automotive ads. Mr. Quadrino, a senior citizen, is selling his car and wants to take out a four-line ad. The paper charges $6.50 per line. What is the price of the ad for Mr. Quadrino?
> Ari purchased a microwave oven on an installment plan for m dollars. He made a 20% down payment and agreed to pay x dollars per month for two years. Express the finance charge (interest) algebraically.
> The Bayside Bugle charges by the word to run automotive ads. The newspaper charges $18 for the first 20 words and $0.35 for each additional word. How much would a 27-word ad cost?
> Ralph placed a classified ad to sell his used SUV for $18,500. After 2 weeks, he didn’t sell the SUV, and the newspaper suggested lowering the price 5%. What would the new price be if Ralph reduced it according to the suggestion?
> Bob wants $50,000 at the end of 7 years in order to buy a car. If his bank pays 1.2% interest, compounded annually, how much must he deposit each year in order to reach his goal?
> Fierro Brothers, a discount broker, charges their customers a $19 flat fee per trade. The Sondo Investment House charges a 2% commission. For what amount of stock would both brokers charge the same commission?
> Samantha purchased a used car for $4,200. Her state charges 4% tax for the car, $47 for registration, $50 for a new title certificate, and $35 for a state safety and emissions inspection. How much does Samantha need to pay for these extra charges, not in
> The Auto Times charges g dollars for a classified ad with m or less lines. Each additional line is d dollars. If x . m, express the cost of an x-line ad algebraically.
> A local newspaper charges g dollars for a four-line classified ad. Each additional line costs d dollars. Write an expression for the cost of a seven-line ad.
> The Antique Auto News charges $10 for a 10-word classified ad. Each additional word costs $0.40. For an extra $40, a seller can include a photo in the ad. How much would a 20-word ad with a photo cost?
> The North Shore News charges $19.50 for a two-line automotive ad. Each additional line costs $7. How much does a six-line ad cost?
> Interpret the quote in the context of what you learned about buying and selling cars in this lesson.
> Bob can afford to deposit $400 a month into a retirement account that compounds interest monthly with an APR of 1.8%. His plan is to have $200,000 saved so that he can then retire. Approximately how long will it take him to reach this goal?
> John is 60 years old. He plans to retire in 2 years. He now has $400,000 in a savings account that yields 2.1% interest compounded monthly. He has calculated that his final working year’s salary will be $88,000. He has been told by his financial advisor
> Fiona opened a retirement account that has an annual rate of 2.2%. She is planning on retiring in 20 years. How much must she deposit into that account each year so that she can have a total of $600,000 by the time she retires?
> Complete the table to find the periodic deposit investment amounts. Future Value Interest Rate Time Deposit $50,000 2%, compounded annually 8 years 4 years a. $25,000 1.5%, compounded semiannually 1.25% compounded quarterly 0.94% compounded monthly
> Laura has been contributing to a retirement account that pays 1.75% interest with pre-tax dollars. This account compounds interest monthly. She has put $500 per month into the account. At the end of 10 years, she needed to pay some medical bills and had
> Mackin Investing charges its customers a 1% commission. The Ross Group, a discount broker, charges $25 per trade. For what amount of stock would both brokers charge the same commission?
> A taxpayer who pays 22% in taxes each year has these two accounts. Account 1: $10,000 is placed in a tax-deferred account that pays 2.1% interest compounded annually for 25 years. Account 2: $10,000 is placed in a taxable account that pays 2.1% interest
> At the age of 30, Jasmine started a retirement account with $50,000, which compounded interest semi-annually with an APR of 1.75%. She made no further deposits. After 25 years, she decided to withdraw 50% of what had accumulated in the account so that sh
> Jay just graduated from college and he has decided to open a retirement account that pays 1.75% interest compounded monthly. If he has direct deposits of $100 per month taken out of his paycheck, how much will he have in the account after 42 years?
> Airline flights can be either discretionary or essential. For most people, the price you pay for where you sit in the plane is a discretionary expense. The seat map for a particular flight is shown here. There are a total of 149 seats on this flight. A
> Ricky is 35 years old. He plans to retire when he is 63. He has opened a traditional retirement account that pays 1% interest compounded monthly. If he makes monthly deposits of $400, how much will he have in the account by the time he retires?
> Is there a difference in the tax in Exercises 17 and 18? If so, how much and which method favors the taxpayer?
> Four people invested in a restaurant. One person invested $100,000. Two others invested in the ratio x:2x, and the fourth person invested an amount equal to the other three investors combined. The total investment was $1,100,000. a. Write an expression
> Ten years ago, Lisa bought a hair salon for x dollars. She built up the business and it is now worth nine times what she paid for it. She decides to sell half of the business to a friend, and they become partners. Express the amount Lisa’s friend must pa
> Complete the table to find the single deposit investment amounts. Future Value Interest Rate Time Deposit 1.4% compounded annually 1.03% compounded semiannually 0.95% compounded quarterly 2.25% compounded monthly $1,000 3 years 5 years 10 years a. $
> Six equal partners own a local pizzeria. The partners have made a tremendous profit and bought many personal items such as cars, boats, new homes, and so on. In order to protect their personal possessions, they decide to incorporate the pizzeria, so that
> Lenny bought x shares of stock for y dollars per share last month. He paid his broker a flat fee of $20. He sold the stock this month for p dollars per share, and paid his broker a 2% commission. Express Lenny’s net proceeds algebraically.
> Mike makes Y dollars per year. His company offers a matching retirement plan in which they agree to match M percent of his contributions up to P percent of his salary. Write an algebraic expression for the maximum value of the employer’s matching contrib
> Nelson makes $120,000 per year. His employer offers a 401(k) plan in which they will match 40% of his contributions up to a maximum of 7% of his annual salary. His employer allows contributions up to a maximum of 15% of Nelson’s salary per year. If Nelso
> Jhanvi is a 40-year-old executive for a department store. She files taxes as head of household. She needed to withdraw $45,000 from her tax-deferred retirement account to put a down payment on a new condominium. Jhanvi’s taxable income
> Mark is an accountant who has been contributing to his retirement account for the last 15 years with pre-tax dollars. The account compounds interest semi-annually at a rate of 2.25%. He contributes x dollars after each 6-month period, and this has not ch
> Jack contributed $400 per month into his retirement account in pre-tax dollars during the last tax year. His taxable income for the year was $62,350. He files taxes as a single taxpayer. a. What would his taxable income have been had he contributed to
> Explain how the quote can be interpreted.
> Decide whether each of the following questions are biased. Explain your decisions with support from the discussion of question bias. a. Do you want a hot dog or your usual chicken sandwich? b. Should smoking be permissible in a person’s own home? c.
> Marcy wants to have $75,000 saved sometime in the future. How much must she deposit into an account that pays 1.3% interest, compounded monthly? Use a graphing calculator to graph the present value function.
> The Frederick Fertilizer Company has developed a fertilizer they think will make plants grow faster, taller, and heartier. They need to conduct an experiment. They need to plant seeds randomly into different containers— some with the fertilizer and some
> A random group of 900 students, from the 5 million students in a certain state, is to be taken using the random number table. a. How many digits will be needed to be assigned to each person? b. Would it be possible for the random sample of 900 student
> For Your Eyes Only manufactures eyeglasses. They have developed a new type of hinge that they plan to test on 300 randomly selected customers. a. If they start on line 30 of the random number table on page 534 of this section, what will be the numbers o
> Laura bought 55 shares of stock for $3.50 per share last year. She paid her broker a 1% commission. She sold the stock this week for $2 per share, and paid her broker a $10 flat fee. a. What were Laura’s net proceeds? Round to the nearest cent. b. What
> An inventor for the Rust-Fight Paint Company wants to test if his paint is more resistant to rust than the current type of paint they manufacture. He will test 10 cans of the old paint and 10 cans of the new paint. a. If he selects the 10 old cans from
> A pharmaceutical company is deciding whether or not to invent a new medication. They need to do some research into physical benefits of certain sports. They want to test if people who only play tennis have lower cholesterol than people who only play golf
> A pharmaceutical company is testing a new drug to see its effectiveness on lowering cholesterol. They randomly select 2,000 people and split them into two groups. The control group takes a placebo—a pill with inactive ingredients—while the other group ta
> A fitness company needs to test some new hand-strengthening equipment, and compare the effectiveness for left and right hands. They need to select 100 volunteers from a gym membership list of 9,876 members. a. If they use the random number table, how ma
> A sole proprietorship is worth w dollars. The owner loses a lawsuit against him for y dollars, where y > w. Express algebraically the value of the personal property the owner must forfeit to pay the settlement.
> A partnership owned equally by 13 partners is worth $1.3 million. The partnership loses a lawsuit worth $3 million. What is the value of any personal property each partner must forfeit to pay the settlement? Explain.
> Jon also noticed that every traditional split ratio can be written in the form x-for-1. Examine how the 3-for-2 traditional split can be expressed as 1.5-for-1. Express each of the following traditional split ratios as x-for-1. Jon noticed that most t
> What is the total value of all of the Bank of America shares traded? PG [email protected] BAC [email protected] DIS 2.55K @95.31V1.08 K [email protected]
> Garden Giant makes rubber garden hoses. The life of their Long Life garden hose is 8.1 years, with a standard deviation of 1.1 years. Their research and development department has come up with a new rubber/plastic compound that they hope will extend hose
> Showstoppers manufactures adhesive vinyl for sign companies. The adhesive loses its adhesion qualities if not used for a few years. The life of their adhesive vinyl is normally distributed with mean 3.5 years and standard deviation 0.4 years. A worker at
> The Kivet Ski Corporation is testing a new safer boot binding for their skis. They need some randomly selected skiers to try the skis to see if the binding is better. Explain how they can design a matched-pairs experiment for this study.
> Interpret the above quote in terms of what you have learned about new inventions in this section.
> Taylor bought 200 shares of stock for $18.12 per share last year. He paid his broker a flat fee of $30. He sold the stock this morning for $21 per share, and paid his broker 0.5% commission. a. What were Taylor’s net proceeds? b. What was his capital g
> The 120 shareholders of a corporation are voting for a new board of directors. Shareholders receive one vote for each share they own. Would it be possible for one shareholder’s votes to choose the new board of directors? Explain.
> Seventy-two percent of the shareholders in a service corporation are women. If the corporation is owned by 45,600 people, how many of the shareholders are women?
> Joe, Thea, and Taylor invested in a partnership in the ratio 1:4:7, respectively. Years later, when the partnership was worth $1.6 million, Thea decides to go to graduate school and sells her part of the partnership to Joe. a. How much would Joe need to
> Julie and Kristen are the partners in a local sporting goods shop. They needed $51,000 to start the business. They invested in the ratio 5:12, respectively. a. How much money did each invest? b. What percent of the business was owned by Kristin? Round
> Elisa owns 28% of Grud man Corp. The rest of the shares are owned equally by the remaining six shareholders. What percent of the corporation does each of the other shareholders own?
> Verify that Jon’s method works to determine the post-split price and shares outstanding for HVC, which executed a 4-for-1 split on July 10 with 22,676,800 outstanding shares and a market price of $203.80 per share before the split. Jon noticed that most
> A corporation issues 1,200,000 shares of stock to shareholders. How many shares must a shareholder own to have a majority of the shares?
> Ryan owns 38 of a florist shop worth $76,000. What is the value of Ryan’s share of the business?
> Tomika owns 35 of a law partnership. What percent of the partnership does she own?
> A private corporation owned by 35 shareholders is worth $1.7 million. The corporation loses a lawsuit worth $3 million. What is the value of any personal property of the shareholders that can be taken to pay the settlement? Explain.
> A corporation is having a shareholders meeting to vote on a new issue. Not all shareholders are able to attend. In fact, most usually do not. The ownership of the corporation is represented by 2,351,000 shares of stock owned by 111,273 shareholders. a.
> The ticker shows trades of stock in Hewlett-Packard (HPQ), Exxon-Mobil (XOM), and Chevron (CVX). a. How many shares of Hewlett-Packard were sold? b. What was the total value of all the HPQ shares sold? c. Joan bought the shares at this price, and her
> The top x shareholders in a corporation each own y shares of a certain stock. The corporation’s ownership is represented by a total of w shares of stock. Express the percent of the corporation owned by the top x shareholders.
> What do you think Thomas Edison meant by the word perspiration? How do those words apply to what you’ve learned about businesses in this lesson?
> Ann obtained this list of apartments. a. Use linear regression analysis to determine if there is a correlation between the square footage and the monthly rent. b. Determine the regression equation. Round the numbers in the equation to the nearest hundr
> Jaden received these two estimates from a moving company. Write and solve a system of equations to determine the hourly loading/unloading fee and the mileage charge for the truck rental. Situation A: He hires five helpers to load and unload the truck and
> Kristy owns 200 shares of Nortel stock. On November 30, the company instituted a 1-for-10 reverse split. The pre-split price per share was $2.15. The number of shares outstanding before the split was 4.34B. a. How many shares did Kristy hold after the s
> A moving helper company gave Mike these two quotes. Use a system of equations to determine the hourly rates for loading/unloading and packing/ unpacking. 3 hours of loading/unloading 5 hours of loading/unloading 2 hours of packing/unpacking 2 hours
> Milena has a gross biweekly income of $2,200. She pays 18% in federal and state taxes, puts aside 10% of her income to pay off her school loan, and puts 5% of her income aside for savings. She is considering an apartment that rents for $1,200 per month.
> Rachel is considering moving into a one-bedroom apartment in Glen Gardens. The apartment has a monthly rent of $1,300. Here are the fees that she has been quoted. How much is she expected to pay up front in order to rent this apartment? Application fee:
> Abe makes $18.50 per hour. He works 37 hours a week. He pays 23% of his gross earnings in federal and state taxes and saves 5% of his monthly gross income. He is considering renting an apartment that will cost $1,500 per month. a. Is this monthly rental
> Jessica’s financial advisor believes she should spend no more than 28% of her gross monthly income for her rent. She has determined that amount is $1,400 per month. Based on this amount and her advisor’s recommendation, what is Jessica’s annual salary?
> Use the interval 25–30% to find the monetary range that is recommended for the monthly rental budget in each situation. Round to the nearest dollar. a. Mark makes $86,000 per year. b. Linda makes $7,000 per month. c. Meghan makes $1,500 per week.
> Carlos does his online trading with Super Trade. Super Trade’s rates are listed in the table below. In a-c, round to the nearest cent. a. If Carlos makes 36 online trades in a year, what is the total of his broker fees? b. What is th
