Math 1 Unit 7 Review

Transcription

1 Name: ate: 1. Which ordered pair is the solution to this system of equations? 5. system of equations is graphed on the set of axes below. y = x + 4 x + y = 2. (1, 5). (0, 2). ( 1, 3). ( 4, 0) 2. Which ordered pair is the solution to this system of equations? 2x y = 10 x + y = 2. (4, 2). (4, 2). (2, 4). ( 4, 2) 3. What is the value of y in the following system of equations? 2x + 3y = 6 2x + y = When solved graphically, which system of equations will have exactly one point of intersection? The solution of this system is. (0, 4). (2, 4). (4, 2). (8, 0) 6. What is the value of x in the solution of the system of equations 3x + 2y = 12 and 5x 2y = 4? y = x 20 y = x y = 3 5 x + 12 y = 0.6x 19. y = 0.5x + 30 y = 0.5x 30. y = x + 15 y = x Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $ Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?. $1.50. $2.00. $3.00. $3.50 page 1

2 8. Mary graphed the system of equations below. y = 3 2 x y = 2 3 x Which of these best describes the relationship between the two lines?. They have no point in common.. They have one point in common.. They have two points in common.. They have infinite points in common. 9. Look at the system of equations below. y = 3 2x + 10 y = 2 3 x 10 Which of these statements is correct?. The system has no solution.. The solution of the system is ( 3, 8).. The solution of the system is (6, 6).. The system has an infinite number of solutions. 10. Which of the following graphs best represents the solution of the system of linear equations shown below? y = x + 4 3x + y = page 2

3 11. Given the system of equations: What is the value of x? 6x + y = 9.7 4x + 2y = system of equations is shown below. y = 5x 2 y = 2x + 4 What is the x-value in the solution to the system of equations? Kerry scored a total of 205 points last season by making a total of 120 baskets. Some of the baskets were 1-point free throws (t), and the rest were 2-point field goals (g). Which pair of equations models this situation?. t + 2g = 205 t + g = 120. t + g = 205 t + g = 120. t + g = 205 t + 2g = 120. t + 2g = 205 t + 2g = Which system of equations represents the statements below? The sum of two numbers is ten. One number is five times the other. 13. The equations of two lines are:. xy = 10 y = 5x. xy = 10 y = x + 5 3x 2y = 11 2x + y = 5. x + y = 10 y = 5x. x + y = 10 y = x + 5 If the lines are graphed, at what point do they intersect?. ( 1, 3). (3, 1). (3, 10). (4, 2 1) 14. system of equations is shown below. 17. The only coins that lexis has are dimes and quarters. Her coins have a total value of $5.80. She has a total of 40 coins. Which of the following systems of equations can be used to find the number of dimes, d, and the number of quarters, q, lexis has? 2x + 2y = 10 5x 2y = 4 What is the solution of the system of equations?. ( 2, 7). (2, 7). (2, 3). (3, 2).... d + q = d + 40q = 5.80 d + q = d q = 5.80 d + q = d q = 40 d + q = d q = 5.80 page 3

4 18. Which graph represents the solution of the system of equations below? y = 3 y = 2x page 4

5 19. Use the information in the box below to answer the question. 21. total of 120 adults and students attended a school volleyball game. Each adult paid $2.50, and each student paid $1.00. The total paid by the adults and students attending the game was $189. Which of the following systems of equations can be used to find a, the number of adults attending, and s, the number of students attending the game? Misha and his sister are using 5-foot and 8-foot landscaping timbers to enclose a vegetable garden. They bought 40 timbers. The total cost for the timbers was $288. Which pair of equations could be used to find the number of timbers of each size that they bought?. 6x + 9y = 40 and x + y = 288. x + y = 40 and 5x + 8y = x + 8y = 40 and 6x + 9y = 288. x + y = 40 and 6x + 9y = Julia and Marcia bought identically priced cans of chili and identically priced jars of salsa to make a dip. Julia bought 3 cans of chili and 2 jars of salsa for $ Marcia bought 2 cans of chili and 4 jars of salsa for $ Which of the following systems of equations could be used to find x, the cost of one can of chili, and y, the cost of one jar of salsa?.... a + s = a + 2.5s = a + s = 120 a + s = a + s = a + 3.5s = 189 a + s = a + s = The only coins that lexis has are dimes and quarters. Her coins have a total value of $5.80. She has a total of 40 coins. Which of the following systems of equations can be used to find the number of dimes, d, and the number of quarters, q, that lexis has?. d + q = d + 40q = d + q = d q = 40. d + q = d q = 40. d + q = d q = Ken and Jerome went to the same electronics store. Ken bought 2 video games and 1 V for a total of $105. Jerome bought 1 video game and 4 Vs for a total of $105.. x + y = x + y = x + 4y = x + 3y = x y = 11 x + y = 11. 3x + 2y = x + 4y = Each video game cost v dollars and each V cost d dollars. Which system of equations can be used to find the cost, in dollars, of each video game and each V at the store?. v + 2d = 105 v + 4d = v + d = 105 v + 4d = v + d = 105 4v + d = v + 4d = 105 v + d = 105 page 5

6 24. The Sanchez family is planning a trip to an amusement park. The park has two ticket plans. Plan offers a weekend pass for $12 plus $0.50 per ride. Plan is $1.25 for each ride. 27. oug and Laura sold cans of soda to raise money for a school dance. oug sold 4 less than 3 times as many cans as Laura. Together they sold 300 cans. Which system of equations could be used to determine d, the number of cans oug sold, and l, the number of cans Laura sold? Let x represent the number of rides each person will ride and y represent the cost per person, in dollars. Which of these systems of equations could be used to choose a ticket plan?. d = 4 3l d + l = 300. d = 3l 4 d + l = 300. d = 3l 4 d + 3l = 300. d = 3l + 4 d + l = 300. y = 0.50x + 12 y = 1.25x. y = 0.50x y = 1.25x. y = 12x y = x y = x + 12 y = x Sam needs to rent a van for a school field trip. Van ompany charges a one-tim fee of $250 plus $10 for each mile driven. Van ompany charges a one-time fee of $150 plus $12 for each mile driven. Let x represent the number of miles driven. Let y represent the total cost, in dollars, to rent the van. Which system of equations models this situation?. y = x y = x. y = 250x + 10 y = 150x y = 10x 250 y = 12x 150. y = 10x y = 12x The tenth-grade class is planning a homecoming dance. They want to hire a band. and : and : The band charges $500 to play for the night. The band charges $275 and $1.50 for each ticket sold. Let n represent the number of tickets sold and c represent the total cost of hiring the band. Which system of equations models this situation?. c = m c = 1.5n c = 500n c = 275n c = 500 c = n c = 500 c = 1.5n In leo s class, g, the number of girls, is 3 times b, the number of boys. There are a total of 28 students in the class. Which system of equations could be used to evaluate this situation to determine the number of boys in leo s class?. b + g = 28 b = 3g. g = 28 + b b = 3g. b = 28 + g g = 3b. b + g = 28 g = 3b 29. The system of equations below shows the rental costs (y), in dollars, for renting a kayak x hours from two different rental companies. y = 25x y = 50x For what number of hours will the rental cost be the same for both companies? The computer lab offers classes after school. In addition to an hourly rate, h, a registration fee, f, is charged. The equations below model the cost for a 2-hour and a 3-hour class. 2h + f = 65 3h + f = 90 What amount is charged for the registration fee?. $15. $25. $30. $40 page 6

7 31. Kara and Sonny went to see a movie at the local theater. Kara paid $13.00 for 1 large box of popcorn and 2 large soft drinks. Sonny paid $8.50 for 1 large box of popcorn and 1 large soft drink. In the system of equations below, p represents the cost of 1 large box of popcorn and s represents the cost of 1 large soft drink. p + 2s = p + s = 8.50 What is the value of p, the cost of 1 large box of popcorn?. $4.00. $4.25. $4.30. $ restaurant needs to set up 7 tables for the 34 members of a high school science club. The restaurant has tables that can seat 4 and tables that can seat 6. This system of equations represents the combination of x, the number of tables for 4, and y, the number of tables for 6, that will seat exactly 34 people. x + y = 7 4x + 6y = 34 How many tables that seat 6 should be set up? Samantha and Maria purchased flowers. Samantha purchased 5 roses for x dollars each and 4 daisies for y dollars each and spent $32 on the flowers. Maria purchased 1 rose for x dollars and 6 daisies for y dollars each and spent $22. The system of equations shown below represents this situation. Which statement is true? 5x + 4y = 32 x + 6y = 22. rose costs $1 more than a daisy.. Samantha spent $4 on each daisy.. Samantha spent more on daisies than she did on roses.. Samantha spent over 4 times as much on daisies as she did on roses. 35. pharmacist mixed some 10%-saline solution with some 15%-saline solution to obtain 100 ml of a 12%-saline solution. How much of the 10%-saline solution did the pharmacist use in the mixture?. 60 ml. 45 ml. 40 ml. 25 ml 36. Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters does she have? 33. nna burned 15 calories per minute running for x minutes and 10 calories per minute hiking for y minutes. She spent a total of 60 minutes running and hiking and burned 700 calories. The system of equations shown below can be used to determine how much time nna spent on each exercise. 15x + 10y = 700 x + y = 60 What is the value of x, the minutes nna spent running? Members of a senior class held a car wash to raise funds for their senior prom. They charged $3 to wash a car and $5 to wash a pick-up truck or a sport utility vehicle. If they earned a total of $275 by washing a total of 75 vehicles, how many cars did they wash? page 7

8 38. flower shop sells the two flower arrangements shown below. 39. The perimeter of a rectangle is 48 inches. The length of the rectangle is 3 times the width of the rectangle. What is the area of the rectangle?. 24 square inches. 54 square inches. 108 square inches. 432 square inches 40. Luke has 15 coins. He has only nickels and dimes. If the total value of the coins is $1.20, how many nickels does he have? Each rose has the same price, and each daisy has the same price. What is the price of one rose?. $3. $6. $9. $12 page 8

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