Pre-Algebra Chapter 7 Solving Equations and Inequalities
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1 Pre-Algebra Chapter 7 Solving Equations and Inequalities SOME NUMBERED QUESTIONS HAVE BEEN DELETED OR REMOVED. YOU WILL NOT BE USING A CALCULATOR FOR PART I MULTIPLE-CHOICE QUESTIONS, AND THEREFORE YOU SHOULD NOT USE ONE FOR THE REVIEW PACKETS. MULTIPLE CHOICE Solve the equation. 1. 2x 26 = 10 A. 8 B. 5 C. 2 D x = 9 A. 1 B. 6 C. 5 D = 4 A. 65 B. 25 C. 5 D x + 6 = 9 A. 3 B. 5 C. 3 D A. 72 B. 9 C. 8 D. 72 A. 4 B. 20 C. 1 D. 4 A. 10 B. 36 C. 10 D. 44 A. 7 B. 11 C. 15 D. 19 A. 28 B. 42 C. 72 D. 84
2 10. A. B. 3 C. D y 3 = 9 A. 48 B. 3 C. 36 D m 7 = 5 A. 4 B. 15 C. 36 D A. 20 B. 9 C. 16 D y + 9 = A. 34 B. 2 C. 9 D A. 10 B. 16 C. 4 D A. B. C. 9 D A. 6 B. 7 C. 8 D x + 5 = 8 A. 40 B. 15 C. 65 D. 15
3 x = A B C D (y + 3) = 4.8 A. 5 B. 3 C. 13 D A. 5 B. 15 C. 2 D. 10 A. 14 B. 7 C. 2 D. 21 A. B. 1 C. 1 D. 24. A. 1 B. 3 C. 3 D Joe wants to buy a video game system for $270. She has $60 and is saving $30 each week. Solve the equation 30w + 60 = 270 to find how many weeks w it will take Joe to save enough to buy the system. A. 6 weeks B. 7 weeks C. 9 weeks D. 8 weeks 26. Brandon needs $480 to buy a TV and stereo system for his room. He received $60 in cash for birthday presents. He plans to save $30 per week from his part-time jo To find how many weeks w it will take to have $480, solve w = 480. A. 16 weeks B. 13 weeks C. 15 weeks D. 14 weeks 27. Mandy and 2 friends bought some mechanical pencils at a special sale. They divided some of the pencils equally among themselves and then gave 3 to Mandy s little brother. At that time they had 19 pencils left. Solve the equation to find the number of pencils p that they bought at the sale. A. 48 pencils B. 57 pencils C. 66 pencils D. 22 pencils 28. Miranda opened a checking account with $560 from her summer jo She withdrew the same amount each week for 13 weeks. Her balance was then $365. Solve the equation to find how much money m she withdrew each week. A. $15 B. $71 C. $39 D. $28
4 29. Work-Out Corner has 5 more than 3 times as many exercise bicycles as The Gym. Together they have 21 bicycles. Solve the equation to find the number of bicycles at Work-Out Corner. A. 4 bicycles B. 17 bicycles C. 7 bicycles D. 25 bicycles 30. The sum of three consecutive integers is 72. Find the integers. A. 22, 23, 24 B. 25, 26, 27 C. 23, 24, 25 D. 24, 25, The 9 officers of the Student Council are going on a trip to an amusement park. Each student must pay an entrance fee plus $5 for meals. The total cost of the trip is $225. Solve the equation to find the cost e of the entrance fee for each student. A. $20 B. $45 C. $25 D. $ Twenty-five members of the eighth grade class at Park Center Middle School are going to a museum and then to lunch. Each student must pay an entrance fee to the museum and $7.25 for lunch. The total cost for the trip is $ What is the entrance fee for one student? A. $10.50 B. $17.46 C. $17.75 D. $ Paul rented a car for $129 plus $0.25 per mile. The total bill at the end of his trip was $ Use the equation x = to find the number of miles he drove. A. 1,382 miles B. 350 miles C. 864 miles D. 607 miles 34. The Party Room at Penny s Pizza rents for an initial fee of $30 and then $5 per hour. Aislyn s bill for her birthday party was $50. For how many hours did she rent the room? A. 6 hours B. 16 hours C. 4 hours D. 10 hours 35. The fare for riding in a taxi is a $3 fixed charge and $0.80 per mile. The fare for a ride of d miles is $6.75. Which equation could be used to find d? A. 3( d) = 3 C d = 6.75 B d = 6.75 D. ( )d = Ms. Baker purchased a number of juice packs at a cost of $0.30 each and a loaf of bread that cost $1.19. The total cost of her purchases was $2.99. Which equation can you use to determine how many juice packs Ms. Baker purchased? A j = 0.30 C. 1.19j j = 2.99 B. 0.30j = 1.19 D. 0.30j = Sheila leaves on a long trip driving at a steady rate of 30 miles per hour. Her sister Allison leaves from the same location traveling to the same destination 2 hours later. She drives at a steady rate of 60 miles per hour. How long after Allison leaves home will she catch up to Sheila? A. 4 hours B. 5 hours C. 3 hours D. 2 hours
5 38. If a number n is subtracted from 25, the result is three less than n. What is the value of n? A. 14 B. 22 C. 28 D Write the given sentence as an equation. Tim s age in 7 years will be three times what it was 19 years ago. A. 3(t + 7) = t 19 C. t + 7 = 3(t 19) B. t + 19 = 3(t 7) D. 3(t + 19) = t 7 Solve and graph the inequality. 40. A. m! 6 C. m " 3 B. m " 6 D. m! A. x > 7 C. x > 2 B. x > 2 D. x < A. x " 0 C. x " 4 B. x! 0 D. x! A. x > 9 C. x > 2 B. x < 2 D. x < 9
6 44. A. x < 4 C. x > 8 B. x! 8 D. x " A. x < 10 C. x > 5 B. x! 0 D. x! A. C. B. D. 47. Melissa wants to spend no more than $300 on school clothes. She spends $75 on a coat and then wants to buy some sweaters that are on special for $10 each. Solve the inequality find the greatest number of sweaters s she can buy. A. 23 sweaters B. 22 sweaters C. 30 sweaters D. 21 sweaters to 48. A small airplane can carry less than 1,050 pounds of luggage and mail. The mail for the day weighs 490 pounds. If each passenger brings 70 pounds of luggage, what is the greatest possible number of passengers that can be taken? A. 15 passengers B. 7 passengers C. 8 passengers D. 9 passengers 49. Four times the sum of a number and 15 is at least 120. Let x represent the number. Find all possible values for x. A. x " 26 B. x " 15 C. x " 15 D. x " 26
7 50. The width of a rectangle is 13 centimeters. Let x represent the length. Find all possible values for x if the perimeter is at least 228 centimeters. A. x " 44 cm B. x " 101 cm C. x " 18 cm D. x " 215 cm 51. Solve the volume formula V = lwh for h. A. B. C. D. 52. Solve the area formula for a circle,, for. A. B. C. D. 53. Solve the perimeter formula for an isosceles triangle,, for A. B. C. D. 54. Solve the area formula for a triangle, bh, for h. A. B. C. D. 55. Solve the area formula for a trapezoid,, for. A. C. B. D. 56. Kendra is planning to ride her bicycle on a popular biking path that is 84 miles long. She plans to average 7 miles per hour. To find about how long the trip will take, solve the distance formula d = rt for t. Then substitute to find the time it will take her for the trip. A. 13 hours B. 12 hours C. 11 hours D. 7 hours 57. The formula for converting degrees Fahrenheit (F) to degrees Celsius (C) is. Find C for F = 5. A. 49 B. 27 C. 3 D. 15
8 58. You drop a rock off a bridge. The rock s height, h (in feet above the water), after t seconds is modeled by. What is the height of the rock after 2 seconds? A. 64 feet B. 605 feet C. 509 feet D. 477 feet 59. The cost of renting a car is given by the formula C = 50n d, where C is the cost in dollars, n is the number of days rental, and d is the distance driven in miles. How much would it cost to rent a car for a 15-day trip, and drive 475 miles each day? A. $1, B. $1, C. $ D. $ Jordan invested $1000 in a savings account. The interest rate is 6% per year. Find the simple interest earned in 4 years. Then find the total of principal plus interest. A. $24,000.00; $25, C. $262.48; $1, B. $60.00; $1, D. $240.00; $1, Andrew invested $1,500 in a certificate of deposit with a simple interest rate of 4%. Find the interest earned in 6 years. Then find the total of principal plus interest. A. $36,000.00; $37, C. $397.98; $1, B. $360.00; $1, D. $60.00; $1, You deposit $500 in an account that earns 5% compounded annually (once per year). What is the balance in your account after 5 years? Round your answer to the nearest cent. A. $2, B. $ C. $ D. $ You deposit $400 in an account that earns 6% compounded annually (once per year). What is the balance in your account after 5 years? Round your answer to the nearest cent. A. $ B. $2, C. $ D. $ Find the balance on a deposit of $1,150 that earns 9% interest compounded annually for 2 years. A. $1, B. $1, C. $2, D. $2, Alecia deposited $500 in a savings account at 5% compounded semiannually. What is her balance after 6 years? A. $ B. $ C. $ D. $897.93
9 SHORT ANSWER 1. Elise and Miguel both collect baseball cards. Miguel has 2 more than 2 times as many cards as Elise. Together they have 971 cards. Write an equation to represent this situation. How many cards does each person have? 2. Caitlin had $402 in her bank account. She withdrew $15 each week to pay for a swimming lesson. She now has $237. Write an equation that can be used to find the number of swimming lessons that she paid for. How many swimming lessons did she pay for? c. At the time she had $237, the cost of a lesson rose to $19. How many lessons can she pay for with her remaining $237? c. 3. Cars For You will rent a car for $11 per day plus $.27 per mile driven. Rent-A-Rama will rent the same car for $26 per day plus $.07 per mile driven. Write an equation that represents the situation when the total rental cost for one day is the same at both rental agencies. For how many miles is the total rental cost for one day the same for each car? c. If you plan to rent a car for one day and drive 100 miles, which rental agency should you choose? c. 4. Jeremy is building a large deck for a community center. The deck is shaped as a rectangle. The width of the deck is 29 feet. The perimeter of the deck is to be at least 134 feet. Write an inequality that represents all possible values for the length of the deck. Find all possible values for the length of the deck.
10 5. Michael is saving money to attend a ski camp in Canad The total cost of the camp is $1,500. He has $785 in a savings account and plans to save $55 per week. Explain how to write an equation to represent this situation. Explain how to solve the equation to find the number of weeks that he will need to save to earn the total amount for the camp. Then find the number of weeks. c. Michael has to pay the entire cost for the camp on June 1. Can he start saving on April 1 and still pay the entire cost? Explain your reasoning. c. 6. Wes owns a shop where he sells souvenirs. He ordered a shipment of boxes of huckleberry chocolates. Only of his order arrived. At that time he had 5 boxes left. Added to the new boxes, he had a total of 128 boxes of the chocolates. Solve the equation to find the number of boxes b that were supposed to be in the shipment. Explain how you solved the equation. Check the solution to the equation from part Explain your method. 7. At the school cafeteria, the cost of one milk is $.50. The total cost of 5 turkey sandwiches and 4 milks is the same as the total cost of 4 turkey sandwiches and 8 milks. Write an equation that can be used to find the cost of a turkey sandwich. Explain what each expression or value represents in the equation. Use the equation you wrote in part to find the cost of a turkey sandwich. Explain how you solved the equation. 8. At Water World the admission fee is $17.00, and you can rent an inner tube for $0.75 per hour. You can use the formula P = h to find the total cost for admission plus renting an inner tube. Solve the formula P = h for h. Explain your steps for solving the formula for h. For how many hours can you rent an inner tube if you only have $20.75 to spend? Explain your method for finding the answer.
11 9. Rudy invested $1, in a savings account earning simple interest. At the end of 3 years, he had a total of $1, in his account. How much simple interest did he earn in 3 years? Explain how you found the answer. How much simple interest did he earn per year? Explain how you found the answer. c. What was the rate of simple interest per year for his account? Explain how you found the answer. c. 10. Solve the equation 3t + 11 = 10. Show that your solution works (check step). 11. Eric buys a skateboard, and his total bill is $ The rate of sales tax was 4%. You can solve the equation s s = to find the cost of the skateboard before tax. Explain what each value or variable in the equation s s = represents in this situation. Solve the equation to find the cost of the skateboard before tax. Explain your method. 12. The Hi-Line School is having an all-school play. The cost of 2 adult and 2 children s tickets is $24. A child s ticket costs half as much as an adult ticket. Write an equation that can be solved to find the cost of an adult ticket. Explain the variables and values you use in the equation. Find the cost of a child s ticket. Explain your method.
12 13. Devin is driving to visit his aunt. He wants to travel at least 540 miles in 9 hours of driving. Write an inequality for this situation. Explain what each term in the inequality represents. Explain how to solve the inequality. Find all possible solutions for this problem. 14. A storage company charges new customers an initial fee of $20.00 for a small unit. Each month of storage costs $ The company wrote a formula for finding the total charge for m months of storage. The formula is T = m, where T is the total cost. Suppose a customer is planning to use the unit for 18 months. What will be the total cost? Show how you find the total cost. Suppose a customer has paid $593.5 for storage. For how many months did the customer use the storage unit? Explain how you found your answer. 15. Scott borrowed $250 from a relative for 9 months. He agrees to pay compound interest at the rate of 4% per month. How much interest will he pay his relative when he returns the money at the end of the 9 months? Explain how you solve this problem. Suppose he has to extend the loan and ends up paying a total of $ For how many months did he borrow the money? Explain how you solve this problem.
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