Additional Exercises 3.1 Express the statement as an algebraic expression. 1. Fifteen divided by a number x. 1. 2. The difference between a number x and 50 2. 3. The cost C decreased by 14% 3. 4. The profit P increased by 12% 4. 5. Thirty-five more than half the weight w 5. 6. One-fourth less than the product of a number x and 5 6. Write the indicated expression. 7. Write an algebraic expression representing the number of cents 7. in n nickels and d dimes. 8. Write an algebraic expression representing the number of seconds 8. in m minutes and s seconds. 9. The number of VCR tapes in a video rental store is 120 more than 9. twice the number of DVDs, d. Write an expression for the number of VCR tapes. 10. The length of a rectangle is 8 inches less than 3 times the width, w. 10. Write an expression for the length. Write an equation to represent the problem. You will need to select a variable. 11. Four times a number decreased by 13 is 11. 11. 12. Four times a number increased by 14 is 42. 12. 13. A number decreased by 12% is 200. 13. 14. A number decreased by 15% is 180. 14. 15. One number is nine greater than six times the other. Their product 15. is 81. 16. One number is four times another. The sum of the two numbers is 24. 16. 17. Maria is seven years older than her sister. The sum of their ages is 13. 17. 18. The sum of two consecutive integers is 51. 18. 19. Lisa is eight years older than her sister. The sum of their ages is 15. 19. 20. One number is three times another. The sum of the two numbers is 24. 20. 88
Additional Exercises 3.2 Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. 1. If the sum of a number and 4 is decreased by 20, the result is 32. 1. 2. If the sum of a number and 5 is increased by 40, the result is 20. 2. 3. If the product of a number and 9 is decreased by 27, the result is 81. 3. 4. If the product of a number and 4 is increased by 12, the result is 8. 4. 5. The sum of three consecutive integers is 252. What is the largest of 5. of the three integers? 6. The sum of two integers is 66. Find the two integers if the larger 6. is 6 less than three times the smaller. 7. The sum of three consecutive integers is 111. What is the largest 7. of the three integers? 8. The sum of two integers is 88. Find the two integers if the larger 8. is 7 less than four times the smaller. 9. A country s rivers contained 645 billion sturgeon. Assuming no 9. new sturgeon enter the country s rivers, and 15 billion are caught each month, how long will it take for the country s rivers to be empty of all sturgeon? 10. Jumbo Warehouse contains 700 billion nuts, bolts, and nails. If no 10. new items are manufactured, and 25 billion are sold each month, how long will it take to empty the warehouse? 11. Garrett has $150 in ten- and twenty-dollar bills. The number of 11. ten-dollar bills is one less than twice the number of twenty-dollar bills. How many of each type bill does Garrett have? 12. Emily has nickels, dimes, and quarters in her piggy bank. She has 12. twice as many dimes as nickels and 12 fewer quarters than dimes. The total value of the coins is $9.00. How many of each coin type does Emily have? 13. A rental company rents garden tillers. The charge for a tiller is $40 13. for the first 5 hours plus $7.50 for each additional hour. If Richard s total rental fee was $92.50, for how long did he have the tiller? 14. The author of a textbook receives 12% of sales as royalties. Find 14. the sales needed if the author wants to earn $75,000 on the book. 15. A country singer was hired to perform a concert at a county rodeo. 15. She was paid $2000 plus 2.5% of admission fees collected at the gate. If the singer received a total of $2590, how much was collected at the gate? 16. Jeff is a salesperson in a retail store and earns $80 per week plus 16. 10% of his weekly sales. If Jeff made $680 one week, what were his sales that week? 89
Additional Exercises 3.2 (cont.) 17. Gail s salary was increased by 30% to $45,500. What was her 17. salary before the increase? 18. In 2005 the federal income tax rate for a person filing a single return 18. with an adjusted gross income between $29,700 and $71,950 was $4,090 plus 25% of the amount in excess of $29,700. If Herman had to pay $11,255 in federal taxes in 2005, what was his adjusted gross income that year? 19. From 2000 to 2006, the number of students enrolled at a state 19. university increased by 40%. If the number of students enrolled at the university in 2006 was 10,325, what was the enrollment in 2000? 20. Between 1996 and 2006, the population of a city decreased by 15%. 20. If the population in 2006 was 361,250, what was the population in 1996. 90
Additional Exercises 3.3 Solve the following geometric problems. 1. Two angles are complementary if the sum of their measures is 90. 1. If angle A and B are complementary angles, and angle A is 9 less than twice angle B, find the measures of angles A and B. 2. Two angles are complementary if the sum of their measures is 90. 2. If angle A and B are complementary angles, and angle A is 6 more than three times angle B, find the measures of angles A and B. 3. Two angles are supplementary if the sum of their measures is 180. 3. If angle A and angle B are supplementary angles, and angle B is 12 more than three times angle A, find the measures of angles A and B. 4. Two angles are supplementary if the sum of their measures is 180. 4. If angle A and angle B are supplementary angles, and angle B is 15 less than twice angle A, find the measures of angles A and B. 5. The sum of the angles of a triangle is 180. If one angle of a triangle 5. is ten degrees larger than the smallest angle and the third angle is 10 less than three times the smallest angle, find the measures of the three angles. 6. In a parallelogram the opposite angles have the same measures and 6. the sum of the angles is 360. If each of the two larger angles in a parallelogram is 30 more than each smaller angle, find the measure of each angle. 7. The perimeter of a rectangle is 240 feet. The length is 20 feet more 7. than the width. What are the dimensions? 8. A triangle has a perimeter of 74 inches. Find the three sides if one 8. side is 24 inches larger than the smallest and the third side is three times the smallest. 9. The length of the base of an isosceles triangle is one third the length 9. of one of its legs. If the perimeter of the triangle is 56 inches, what is the length of the base? 10. The perimeter of a rectangle is 200 feet. The width is two-thirds as 10. long as the length. What are the dimensions of the rectangle? 11. The length of an official NBA basketball court is 6 feet less than 11. twice the width. The perimeter is 288 feet. Find the dimensions of the court. 12. The width of an official volleyball court is half its length. The 12. perimeter is 54 meters. Find the dimensions of the court. 13. A triangle has a perimeter of 71 inches. Find the three sides if one 13. side is 31 inches larger than the smallest and the third side is three times the smallest. 14. The length of the base of an isosceles triangle is one fourth the 14. length of one of its legs. If the perimeter of the triangle is 90 cm, what is the length of the base? 91
Additional Exercises 3.3 (cont.) 15. A book case is to have four shelves including the top and bottom. 15. The height of the book case is to be 2.5 feet more than the width. Find the width and height of the book case if only 26 feet of lumber is available. 16. A book case is to have four shelves including the top. The height of 16. the book case is to be 4.25 feet more than the width. Find the width and height of the book case if only 31 feet of lumber is available. 17. An official Major League Baseball diamond is actually a square 17. with a perimeter of 360 feet. Find the dimensions of the diamond. 18. The outer perimeter of the Pentagon building in Washington, D.C. 18. (which houses the U.S. Department of Defense) is 1400 meters. The building is a regular pentagon, which means its five sides are equal in length. Find the length of each outer wall. 19. Steve and Mimi are placing a border around a rectangular flower bed. 19. One long side will be next to the house and will not have a border. The longer side is to be 3 feet more than the shorter side, and they have 24 feet of border material. Find the length and width of the flower bed. 20. A rectangular room has a 25 yard strip of wallpaper bordering it 20. near the ceiling. If the room is 8 yards long, what is its width? 92
Additional Exercises 3.4 1. A bus travels 150 miles on 10 gallons of gas. How many gallons 1. will it need to travel 225 miles? 2. Marsha can check 13 parts per minute on an assembly line. How 2. many parts will she be able to check in 3 hours? 3. On the first day of their vacation trip the Lopez family traveled 407 3. miles in 11 hours. What was their average speed? 4. On the fifth day of their vacation trip the Lopez family traveled 4. 216 miles in 6 hours. What was their average speed? 5. A van travels 200 miles on 10 gallons of gas. How many gallons 5. will it need to travel 340 miles? 6. An SUV gets 15 miles per gallon of gasoline. If its tank will hold 6. 22 gallons, how far can the SUV travel on a tank of gas? 7. One day, John worked for 6.5 hours and was paid $92.95. How 7. long did John work the following day if he was paid $114.40? 8. A train traveling at 40 miles per hour leaves for a certain town. One 8. hour later, a bus traveling at 50 miles per hour leaves for the same town and arrives at the same time as the train. If both the train and the bus traveled in a straight line, how far is the town from where they started? 9. Train A leaves a station traveling at 40 mph. Eight hours later, train 9. B leaves the same station traveling in the same direction at 60 mph. How long does it take for train B to catch up to train A? 10. Two trains leave the same station precisely at noon. One train heads 10. due east at 45 miles per hour while the other train heads due west at at 55 miles per hour. At what time will the two trains be 40 miles apart? 11. Two trains, an express and a commuter, are 450 miles apart. 11. Both start at the same time and travel toward each other. They meet 6 hours later. The speed of the express is 25 miles per hour faster than the commuter. Find the speed of each train. 12. George invested $19,000 for one year, part at 11% and part at 12. 12%. If he earned a total interest of $2200, how much was invested at each rate? 13. Cindy invested $24,000 for one year, part at 6% and part at 9%. 13. If she earned a total interest of $1740, how much was invested at each rate? 14. How many liters of 18% salt solution must be added to 92 liters 14. of 61% salt solution to get a 41% salt solution? 15. How many pounds of coffee beans selling for $2.80 per pound 15. should be mixed with 2 pounds of coffee beans selling for $1.60 a pound to obtain a mixture selling for $2.56 per pound? 93
Additional Exercises 3.4 (cont.) 16. How many pounds of salted nuts selling for $3.00 per pound should 16. be mixed with 7 pounds of salted nuts selling for $1.20 a pound to obtain a mixture selling for $1.74 per pound? 17. A chemist needs 600 milliliters of a 31% alcohol solution. To obtain 17. this solution, how much of a 10% alcohol solution should be mixed with a 40% alcohol solution? 18. Susan charges $25 for a 30-minute private violin lesson. She 18. charges $15 per student for a 60-minute group violin lesson. One day Susan earned $245 from 13 students. How many students did she see for private lessons and how many did she see in the group lesson? 19. How many pounds of gourmet candy selling for $2.40 per pound 19. should be mixed with 3 pounds of gourmet candy selling for $1.20 a pound to obtain a mixture selling for $2.04 per pound? 20. How many pounds of gourmet candy selling for $2.00 per pound 20. should be mixed with 2 pounds of gourmet candy selling for $3.00 per pound to obtain a mixture selling for $2.20 per pound? 94