In a basketball game, the Bulldogs scored 34 field goals,

In Exercises 1–4, what necessary piece of information is missing that prevents solving the problem? If a student saves $35 per week, how long will it take to save enough money to buy a computer?

In Exercises 1–4, what necessary piece of information is missing that prevents solving the problem? If a steak sells for $8.15, what is the cost per pound?

In Exercises 1–4, what necessary piece of information is missing that prevents solving the problem? If it takes you 4 minutes to read a page in a book, how many words can you read in one minute?

In Exercises 1–4, what necessary piece of information is missing that prevents solving the problem? By paying $1500 cash and the balance in equal monthly payments, how many months would it take to pay for a car costing $12,495?

In Exercises 5–8, one more piece of information is given than is necessary for solving the problem. Identify this unnecessary piece of information. Then solve the problem. A salesperson receives a weekly salary of $350. In addition, $15 is paid for every item sold in excess of 200 items. How much extra is received from the sale of 212 items?

In Exercises 5–8, one more piece of information is given than is necessary for solving the problem. Identify this unnecessary piece of information. Then solve the problem. You have $250 to spend and you need to purchase four new tires. If each tire weighs 21 pounds and costs $42 plus $2.50 tax, how much money will you have left after buying the tires?

In Exercises 5–8, one more piece of information is given than is necessary for solving the problem. Identify this unnecessary piece of information. Then solve the problem. A parking garage charges $2.50 for the first hour and $0.50 for each additional hour. If a customer gave the parking attendant $20.00 for parking from 10 a.m. to 3 p.m., how much did the garage charge?

In Exercises 5–8, one more piece of information is given than is necessary for solving the problem. Identify this unnecessary piece of information. Then solve the problem. An architect is designing a house. The scale on the plan is 1 inch = 6 feet. If the house is to have a length of 90 feet and a width of 30 feet, how long will the line representing the house’s length be on the blueprint?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. a. Which is the better value: a 15.3-ounce box of cereal for $3.37 or a 24-ounce box of cereal for $4.59? b. The supermarket displays the unit price for the 15.3-ounce box in terms of cost per ounce, but displays the unit price for the 24-ounce box in terms of cost per pound. What are the unit prices, to the nearest cent, given by the supermarket? c. Based on your work in parts (a) and (b), does the better value always have the lower displayed unit price? Explain your answer.

Use Polya’s four-step method in problem solving to solve Exercises 9–40. a. Which is the better value: a 12-ounce jar of honey for $2.25 or an 18-ounce jar of honey for $3.24? b. The supermarket displays the unit price for the 12-ounce jar in terms of cost per ounce, but displays the unit price for the 18-ounce jar in terms of cost per quart. Assuming 32 ounces in a quart, what are the unit prices, to the nearest cent, given by the supermarket? c. Based on your work in parts (a) and (b), does the better value always have the lower displayed unit price? Explain your answer.

Use Polya’s four-step method in problem solving to solve Exercises 9–40. One person earns $48,000 per year. Another earns $3750 per month. How much more does the first person earn in a year than the second?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. At the beginning of a year, the odometer on a car read 25,124 miles. At the end of the year, it read 37,364 miles. If the car averaged 24 miles per gallon, how many gallons of gasoline did it use during the year?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. A television sells for $750. Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $100 down and $50 a month for 14 months. How much is saved by paying the total amount at the time of the purchase?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. In a basketball game, the Bulldogs scored 34 field goals, each counting 2 points, and 13 foul goals, each counting 1 point. The Panthers scored 38 field goals and 8 foul goals. Which team won? By how many points did it win?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. Calculators were purchased at $65 per dozen and sold at $20 for three calculators. Find the profit on six dozen calculators.

Use Polya’s four-step method in problem solving to solve Exercises 9–40. Pens are bought at $0.95 per dozen and sold in groups of four for $2.25. Find the profit on 15 dozen pens.

Use Polya’s four-step method in problem solving to solve Exercises 9–40. Each day a small business owner sells 200 pizza slices at $1.50 per slice and 85 sandwiches at $2.50 each. If business expenses come to $60 per day, what is the owner’s profit for a 10-day period?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. A college tutoring center pays math tutors $8.15 per hour. Tutors earn an additional $2.20 per hour for each hour over 40 hours per week. A math tutor worked 42 hours one week and 45 hours the second week. How much did the tutor earn in this two-week period?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. A car rents for $220 per week plus $0.25 per mile. Find the rental cost for a two-week trip of 500 miles for a group of three people.

Use Polya’s four-step method in problem solving to solve Exercises 9–40. A college graduate receives a salary of $2750 a month for her first job. During the year she plans to spend $4800 for rent, $8200 for food, $3750 for clothing, $4250 for household expenses, and $3000 for other expenses. With the money that is left, she expects to buy as many shares of stock at $375 per share as possible. How many shares will she be able to buy?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. Charlene decided to ride her bike from her home to visit her friend Danny. Three miles away from home, her bike got a flat tire and she had to walk the remaining two miles to Danny’s home. She could not repair the tire and had to walk all the way back home. How many more miles did Charlene walk than she rode?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. A store received 200 containers of juice to be sold by April 1. Each container cost the store $0.75 and sold for $1.25. The store signed a contract with the manufacturer in which the manufacturer agreed to a $0.50 refund for every container not sold by April 1. If 150 containers were sold by April 1, how much profit did the store make?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. A storeowner ordered 25 calculators that cost $30 each. The store owner can sell each calculator for $35. The store owner sold 22 calculators to customers. He had to return 3 calculators and pay a $2 charge for each returned calculator. Find the store owner's profit.

Use Polya’s four-step method in problem solving to solve Exercises 9–40. New York City and Washington, D.C. are about 240 miles apart. A car leaves New York City at noon traveling directly south toward Washington, D.C. at 55 miles per hour. At the same time and along the same route, a second car leaves Washington, D.C. bound for New York City traveling directly north at 45 miles per hour. How far has each car traveled when the drivers meet for lunch at 2:24 p.m.?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. An automobile purchased for $23,000 is worth $2700 after 7 years. Assuming that the car’s value depreciated steadily from year to year, what was it worth at the end of the third year?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. An automobile purchased for $34,800 is worth $8550 after 7 years. Assuming that the car’s value depreciated steadily from year to year, what was it worth at the end of the third year?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. An automobile purchased for $34,800 is worth $8550 after 7 years. Assuming that the car’s value depreciated steadily from year to year, what was it worth at the end of the third year?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. How many ways can you make change for a quarter using only pennies, nickels, and dimes?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. The members of the Student Activity Council on your campus are meeting to select two speakers for a month-long event celebrating artists and entertainers. The choices are Johnny Depp, Jamie Foxx, Jon Stewart, and Hilary Swank. How many different ways can the two speakers be selected?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. The members of the Student Activity Council on your campus are meeting to select two speakers for a month-long event exploring why some people are most likely to succeed. The choices are Bill Clinton, Sean Combs, Donald Trump, Oprah Winfrey, and Tiger Woods. How many different ways can the two speakers be selected?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. If you spend $4.79, in how many ways can you receive change from a five-dollar bill?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. If you spend $4.79, in how many ways can you receive change from a five-dollar bill?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. You throw three darts at the board shown. Each dart hits the board and scores a 1, 5, or 10. How many different total scores can you make?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. Suppose that you throw four darts at the board shown. With these four darts, there are 16 ways to hit four different numbers whose sum is 100. Describe one way you can hit four different numbers on the board that total 100.

Use Polya’s four-step method in problem solving to solve Exercises 9–40. Five housemates (A, B, C, D, and E) agreed to share the expenses of a party equally. If A spent $42, B spent $10, C spent $26, D spent $32, and E spent $30, who owes money after the party and how much do they owe? To whom is money owed, and how much should they receive? In order to resolve these discrepancies, who should pay how much to whom?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. Six houses are spaced equally around a circular road. If it takes 10 minutes to walk from the first house to the third house, how long would it take to walk all the way around the road?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. If a test has four true/false questions, in how many ways can there be three answers that are false and one answer that is true?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. There are five people in a room. Each person shakes the hand of every other person exactly once. How many handshakes are exchanged?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. Five runners, Andy, Beth, Caleb, Darnell, and Ella, are in a one-mile race. Andy finished the race 7 seconds before Caleb. Caleb finished the race 2 seconds before Beth. Beth finished the race 6 seconds after Darnell. Ella finished the race 8 seconds after Darnell. In which order did the runners finish the race?

Use Polya’s four-step method in problem solving to solve Exercises 9–40. Eight teams are competing in a volleyball tournament. Any team that loses a game is eliminated from the tournament. How many games must be played to determine the tournament winner?

In Exercises 41–42, you have three errands to run around town, although in no particular order. You plan to start and end at home. You must go to the bank, the post office, and the dry cleaners. Distances, in miles, between any two of these locations are given in the diagram. Determine a route whose distance is less than 12 miles for running the errands and returning home.

In Exercises 41–42, you have three errands to run around town, although in no particular order. You plan to start and end at home. You must go to the bank, the post office, and the dry cleaners. Distances, in miles, between any two of these locations are given in the diagram. Determine a route whose distance exceeds 12 miles for running the errands and returning home.

The map shows five western states. Trace a route on the map that crosses each common state border exactly once.

The layout of a city with land masses and bridges is shown. Trace a route that shows people how to walk through the city so as to cross each bridge exactly once.

Jose, Bob, and Tony are college students living in adjacent dorm rooms. Bob lives in the middle dorm room. Their majors are business, psychology, and biology, although not necessarily in that order. The business major frequently uses the new computer in Bobs dorm room when Bob is in class. The psychology major and Jose both have 8 a.m. classes, and the psychology major knocks on Joses wall to make sure he is awake. Determine Bobs major.

The figure represents a map of 13 countries. If countries that share a common border cannot be the same color, what is the minimum number of colors needed to color the map?

The sudoku (pronounced: sue-DOE-koo) craze, a number puzzle popular in Japan, hit the United States in 2005. A sudoku (“single number”) puzzle consists of a 9-by-9 grid of 81 boxes subdivided into nine 3-by-3 squares. Some of the square boxes contain numbers. Here is an example: The objective is to fill in the remaining squares so that every row, every column, and every 3-by-3 square contains each of the digits from 1 through 9 exactly once. (You can work this puzzle in Exercise 66, perhaps consulting one of the dozens of sudoku books in which the numerals 1 through 9 have created a cottage industry for publishers. There’s even a Sudoku for Dummies.) Trying to slot numbers into small checkerboard grids is not unique to sudoku. In Exercises 47–50, we explore some of the intricate patterns in other arrays of numbers, including magic squares. A magic square is a square array of numbers arranged so that the numbers in all rows, all columns, and the two diagonals have the same sum. Here is an example of a magic square in which the sum of the numbers in each row, each column, and each diagonal is 15: Exercises 47–48 are based on magic squares. (Be sure you have read the preceding discussion.) a. Use the properties of a magic square to fill in the missing numbers. b. Show that the number of letters in the word for each number in the square in part (a) generates another magic square.

The sudoku (pronounced: sue-DOE-koo) craze, a number puzzle popular in Japan, hit the United States in 2005. A sudoku (“single number”) puzzle consists of a 9-by-9 grid of 81 boxes subdivided into nine 3-by-3 squares. Some of the square boxes contain numbers. Here is an example: The objective is to fill in the remaining squares so that every row, every column, and every 3-by-3 square contains each of the digits from 1 through 9 exactly once. (You can work this puzzle in Exercise 66, perhaps consulting one of the dozens of sudoku books in which the numerals 1 through 9 have created a cottage industry for publishers. There’s even a Sudoku for Dummies.) Trying to slot numbers into small checkerboard grids is not unique to sudoku. In Exercises 47–50, we explore some of the intricate patterns in other arrays of numbers, including magic squares. A magic square is a square array of numbers arranged so that the numbers in all rows, all columns, and the two diagonals have the same sum. Here is an example of a magic square in which the sum of the numbers in each row, each column, and each diagonal is 15: Exercises 47–48 are based on magic squares. (Be sure you have read the preceding discussion.) a. Use the properties of a magic square to fill in the missing numbers. b. Show that if you reverse the digits for each number in the square in part (a), another magic square is generated. (Source for the alpha magic square in Exercise 47 and the mirror magic square in Exercise 48: Clifford A. Pickover, A Passion for Mathematics, John Wiley & Sons, Inc., 2005)

The sudoku (pronounced: sue-DOE-koo) craze, a number puzzle popular in Japan, hit the United States in 2005. A sudoku (“single number”) puzzle consists of a 9-by-9 grid of 81 boxes subdivided into nine 3-by-3 squares. Some of the square boxes contain numbers. Here is an example: The objective is to fill in the remaining squares so that every row, every column, and every 3-by-3 square contains each of the digits from 1 through 9 exactly once. (You can work this puzzle in Exercise 66, perhaps consulting one of the dozens of sudoku books in which the numerals 1 through 9 have created a cottage industry for publishers. There’s even a Sudoku for Dummies.) Trying to slot numbers into small checkerboard grids is not unique to sudoku. In Exercises 47–50, we explore some of the intricate patterns in other arrays of numbers, including magic squares. A magic square is a square array of numbers arranged so that the numbers in all rows, all columns, and the two diagonals have the same sum. Here is an example of a magic square in which the sum of the numbers in each row, each column, and each diagonal is 15: As in sudoku, fill in the missing numbers in the 3-by-3 square so that it contains each of the digits from 1 through 9 exactly once. Furthermore, in this antimagic square, the rows, the columns, and the two diagonals must have different sums.

The sudoku (pronounced: sue-DOE-koo) craze, a number puzzle popular in Japan, hit the United States in 2005. A sudoku (“single number”) puzzle consists of a 9-by-9 grid of 81 boxes subdivided into nine 3-by-3 squares. Some of the square boxes contain numbers. Here is an example: The objective is to fill in the remaining squares so that every row, every column, and every 3-by-3 square contains each of the digits from 1 through 9 exactly once. (You can work this puzzle in Exercise 66, perhaps consulting one of the dozens of sudoku books in which the numerals 1 through 9 have created a cottage industry for publishers. There’s even a Sudoku for Dummies.) Trying to slot numbers into small checkerboard grids is not unique to sudoku. In Exercises 47–50, we explore some of the intricate patterns in other arrays of numbers, including magic squares. A magic square is a square array of numbers arranged so that the numbers in all rows, all columns, and the two diagonals have the same sum. Here is an example of a magic square in which the sum of the numbers in each row, each column, and each diagonal is 15: The missing numbers in the 4-by-4 array are one-digit numbers. The sums for each row, each column, and one diagonal are listed in the voice balloons outside the array. Find the missing numbers.

Some numbers in the printing of a division problem have become illegible. They are designated below by *. Fill in the blanks. \(\begin{array}{c}\ \ \ \ \ \ \ 1**\\ **\longdiv{4***}\\ \frac{28}{*56}\\ \frac{***}{\ \ \ \ ***}\\ \ \ \ \frac{***}{\ \ \ \ 0}\end{array}\) Text Transcription: 1** ** longdiv 4*** 28/*56 ***/*** ***/0

In Exercises 52–54, explain the plan needed to solve the problem. If you know how much was paid for several pounds of steak, find the cost of one pound.

In Exercises 52–54, explain the plan needed to solve the problem. If you know a person’s age, find the year in which that person was born.

In Exercises 52–54, explain the plan needed to solve the problem. If you know how much you earn each hour, find your yearly income.

Write your own problem that can be solved using the fourstep procedure. Then use the four steps to solve the problem.

Make Sense? In Exercises 56–59, determine whether each statement makes sense or does not make sense, and explain your reasoning. Polya’s four steps in problem solving make it possible for me to solve any mathematical problem easily and quickly.

Make Sense? In Exercises 56–59, determine whether each statement makes sense or does not make sense, and explain your reasoning. I used Polya’s four steps in problem solving to deal with a personal problem in need of a creative solution.

Make Sense? In Exercises 56–59, determine whether each statement makes sense or does not make sense, and explain your reasoning. I find it helpful to begin the problem-solving process by restating the problem in my own words.

Make Sense? In Exercises 56–59, determine whether each statement makes sense or does not make sense, and explain your reasoning. When I get bogged down with a problem, there’s no limit to the amount of time I should spend trying to solve it.

Gym lockers are to be numbered from 1 through 99 using metal numbers to be nailed onto each locker. How many 7s are needed?

You are on vacation in an isolated town. Everyone in the town was born there and has never left. You develop a toothache and check out the two dentists in town. One dentist has gorgeous teeth and one has teeth that show the effects of poor dental work. Which dentist should you choose and why?

India Jones is standing on a large rock in the middle of a square pool filled with hungry, man-eating piranhas. The edge of the pool is 20 feet away from the rock. India’s mom wants to rescue her son, but she is standing on the edge of the pool with only two planks, each \(19 \frac{1}{2}\) feet long. How can India be rescued using the two planks? Text Transcription: 19 1/2

One person tells the truth on Monday, Tuesday, Wednesday, and Thursday, but lies on all other days. A second person lies on Tuesday, Wednesday, and Thursday, but tells the truth on all other days. If both people state I lied yesterday, then what day of the week is it today?

(This logic problem dates back to the eighth century.) A farmer needs to take his goat, wolf, and cabbage across a stream. His boat can hold him and one other passenger (the goat, wolf, or cabbage). If he takes the wolf with him, the goat will eat the cabbage. If he takes the cabbage, the wolf will eat the goat. Only when the farmer is present are the cabbage and goat safe from their respective predators. How does the farmer get everything across the stream?

As in sudoku, fill in the missing numbers along the sides of the triangle so that it contains each of the digits from 1 through 9 exactly once. Furthermore, each side of the triangle should contain four digits whose sum is 17.

Solve the sudoku puzzle in the middle of the left column on page 40.

A version of this problem, called the missing dollar problem, first appeared in 1933. Three people eat at a restaurant and receive a total bill for $30. They divide the amount equally and pay $10 each. The waiter gives the bill and the $30 to the manager, who realizes there is an error: The correct charge should be only $25. The manager gives the waiter five $1 bills to return to the customers, with the restaurants apologies. However, the waiter is dishonest, keeping $2 and giving back only $3 to the customers. In conclusion, each of the three customers has paid $9 and the waiter has stolen $2, giving a total of $29. However, the original bill was $30. Where has the missing dollar gone?

A firefighter spraying water on a fire stood on the middle rung of a ladder. When the smoke became less thick, the firefighter moved up 4 rungs. However it got too hot, so the firefighter backed down 6 rungs. Later, the firefighter went up 7 rungs and stayed until the fire was out. Then, the firefighter climbed the remaining 4 rungs and entered the building. How many rungs does the ladder have?

The Republic of Margaritaville is composed of four states: A, B, C, and D. According to the country’s constitution, the congress will have 30 seats, divided among the four states according to their respective populations. The table shows each state’s population. Allocate the 30 congressional seats among the four states in a fair manner.

Exercises 70–74 describe problems that have many plans for finding an answer. Group members should describe how the four steps in problem solving can be applied to find a solution. It is not necessary to actually solve each problem. Your professor will let the group know if the four steps should be described verbally by a group spokesperson or in essay form. How much will it cost to install bicycle racks on campus to encourage students to use bikes, rather than cars, to get to campus?

Exercises 70–74 describe problems that have many plans for finding an answer. Group members should describe how the four steps in problem solving can be applied to find a solution. It is not necessary to actually solve each problem. Your professor will let the group know if the four steps should be described verbally by a group spokesperson or in essay form. How many new counselors are needed on campus to prevent students from waiting in long lines for academic advising?

Exercises 70–74 describe problems that have many plans for finding an answer. Group members should describe how the four steps in problem solving can be applied to find a solution. It is not necessary to actually solve each problem. Your professor will let the group know if the four steps should be described verbally by a group spokesperson or in essay form. By how much would taxes in your state have to be increased to cut tuition at community colleges and state universities in half?

Exercises 70–74 describe problems that have many plans for finding an answer. Group members should describe how the four steps in problem solving can be applied to find a solution. It is not necessary to actually solve each problem. Your professor will let the group know if the four steps should be described verbally by a group spokesperson or in essay form. Is your local electric company overcharging its customers?

Exercises 70–74 describe problems that have many plans for finding an answer. Group members should describe how the four steps in problem solving can be applied to find a solution. It is not necessary to actually solve each problem. Your professor will let the group know if the four steps should be described verbally by a group spokesperson or in essay form. Should solar heating be required for all new construction in your community?

Exercises 70–74 describe problems that have many plans for finding an answer. Group members should describe how the four steps in problem solving can be applied to find a solution. It is not necessary to actually solve each problem. Your professor will let the group know if the four steps should be described verbally by a group spokesperson or in essay form. Group members should describe a problem in need of a solution. Then, as in Exercises 70–74, describe how the four steps in problem solving can be applied to find a solution.