Chapter 1

In Exercises 1-8, find a counterexample to show that each of the statements is false. The sum of two three-digit numbers is a four-digit number.

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 1-8, find a counterexample to show that each of the statements is false. Adding the same number to both the numerator and the denominator (top and bottom) of a fraction does not change the fraction's value.

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 1-8, find a counterexample to show that each of the statements is false. If the difference between two numbers is odd, then the two numbers are both odd.

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 1-8, find a counterexample to show that each of the statements is false. If a number is added to itself, the sum is greater than the original number.

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 9-44. 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.

In Exercises 9-22, obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(359+596\)

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(8,12,16,20,24\),_____

Use Polya's four-step method in problem solving to solve Exercises 9-44. 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.

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(19,24,29,34,39\),_____

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?

In Exercises 9-22, obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(8.93+1.04+19.26\)

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(37,32,27,22,17\),______

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?

In Exercises 9-22, obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(7.92+3.06+24.36\)

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) 1\(33,29,25,21,17\),_____

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(3,9,27,81,243\), _____

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(2,8,32,128,512\), _____

In Exercises 9-22, obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(39.67 \times 5.5\)

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(1,2,4,8,16\),_

In Exercises 9-22, obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(78.92 \times 6.5\)

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(1,5,25,125\), ____

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?

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(1,4,1,8,1,16,1\),_____

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?

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(1,4,1,7,1,10,1\),_____

Calculators were purchased at \(\$ 65\) per dozen and sold at \(\$ 20\) for three calculators. Find the profit on six dozen calculators.

In Exercises 9-22, obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(47.83 \div 2.9\)

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(4,2,0,-2,-4\),_____

Pens are bought at \(\$ 0.95\) per dozen and sold in groups of four for \(\$ 2.25\). Find the profit on 15 dozen pens.

In Exercises 9-22, obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(54.63 \div 4.7\)

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(6,3,0,-3,-6\),_____

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?

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(\frac{1}{2}, \frac{1}{6}, \frac{1}{10}, \frac{1}{14}, \frac{1}{18}\),_____

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?

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}\),_____

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.

In Exercises 23-34, determine each estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? Estimate the total cost of six grocery items if their prices are \(\$ 3.47, \$ 5.89, \$ 19.98, \$ 2.03, \$ 11.85\), and \(\$ 0.23\).

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27}\),_____

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?

Estimate the total cost of six grocery items if their prices are \(\$ 4.23, \$ 7.79, \$ 28.97, \$ 4.06, \$ 13.43\), and \(\$ 0.74\).

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}\),_____

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?

A full-time employee who works 40 hours per week earns \(\$ 19.50\) per hour. Estimate that person's annual income.

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(3,7,12,18,25,33\),_____

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?

A full-time employee who works 40 hours per week earns \(\$ 29.85\) per hour. Estimate that person's annual income.