The Mild and Wild Amusement Park



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Using Matrices to Solve Higher-Order Systems

Part 1: The Basics

Use matrices to solve each system below.

|1. |3m + 4n = -14 |2. |2x – y + 2z = 15 |

| |-2m – 3n = 11 | |-x + y + z = 3 |

| | | |3x – y + 2z = 18 |

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|3. |3x – 2y + 4z = 15 |4. |2a + 3b + 4c = 2 |

| |x – y + z = 3 | |5a – 2b + 3c = 0 |

| |x + 4y – 5z = 0 | |a – 5b – 2c = -4 |

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|5. |2d + e – f = -8 |6. |2x – 5y + z = 5 |

| |4d – e + 2f = -3 | |3x + 2y – z = 17 |

| |-3d + e + 2f = 5 | |4x – 3y + 2z = 17 |

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|7. |x – 4y + 3z = -27 |8. |a + b = 3 |

| |2x + 2y – 3z = 22 | |-b + c = 3 |

| |4z = -16 | |a + 2c = 10 |

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|9. |p + 4r = -7 |10. |w – 5x + 2y – z = -18 |

| |p – 3q = -8 | |3w + x – 3y + 2z = 17 |

| |q + r = 1 | |4w – 2x + y – z = -1 |

| | | |-2w + 3x – y + 4z = 11 |

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Part 2: The dreaded word problems

For each problem, write a system of equations. Then, use matrices to solve the system. State the answer to the problem with appropriate units.

11. On a recent trip to the movies to see the Matrix, three students – Mark, Carly, and Rita – each spent some money at the concession counter. Mark bought two candy bars, a drink, and two bags of popcorn for a total of $5.35. Carly spent $4.16 on a candy bar, two small drinks, and a bag of popcorn. Meanwhile, Rita spent $5.85. She didn’t buy any candy, but she bought two small drinks and three bags of popcorn. If all the purchases included tax, what was the purchase price for each item?

12. The Baseball Shoppe sold 10 balls, 3 bats, and 2 bases for $99 on Monday; 4 balls, 8 bats, and 2 bases for $78 on Tuesday; and 2 balls, 3 bats, and 1 base for $33.60 on Wednesday. What is the price of each ball, bat, and base?

13. Three friends, Travis, Kaitlyn, and Carmen, plan to spend the day at the Mild and Wild Amusement Park. Each of the rides at the park is classified as “Mild,” “Wild,” or “Super Wild;” the ticket price for each type of ride is different. By the end of their day at the amusement park, Travis had ridden 4 Mild rides, 8 Wild rides, and 8 Super Wild rides for a total ticket cost of $26.00. Kaitlyn had ridden 8 Mild rides, 7 Wild rides, and 5 Super Wild rides for a total ticket cost of $24.25. Carmen had ridden 7 Mild rides, 6 Wild rides, and 4 Super Wild rides for a total ticket cost of $20.50. If a fourth friend went to park and rode 3 Mild rides, 5 Wild rides, and 8 Super Wild rides, how much money would he have spent on ride tickets?

14. Find the measures of the three angles of a triangle if twice the measure of the first angle plus three times the measure of the second angle equals the measure of the third angle, and if the measure of the second angle is 3 degrees more than the measure of the first angle. (Don’t forget the sum of the measures of the angles of a triangle is …)

15. The sum of three numbers is 6. The third number is the sum of the first and second number. The first number is one more than the third number. Find the three numbers.

16. The sum of three numbers is -4. The second number decreased by the third is equal to the first. The sum of the first and second number is -5. Find the three numbers.

17. Julio and offensive line from the MacGregor football team went to Burger World three times in the last week and each time ordered several of the same three items. The first visit resulted in a bill of $25.24 after ordering 3 hamburgers, 5 double cheeseburgers, and 6 Jumbo burgers. The second visit they ordered 2 hamburgers, 7 double cheeseburgers, and 5 Jumbo burgers for a total of $25.68. The third visit their bill was $26.59 when they ordered 4 hamburgers, 4 double cheeseburgers, and 7 Jumbo burgers. Their coach did not go with them on the first three trips and wants to know how much each burger costs. What is the price of each kind of burger?

18. Three kinds of tickets were sold for a concert. Main floor tickets cost $35, balcony tickets cost $25, and gallery tickets cost $15. The box office sold 475 tickets to the concert for a total of $13, 275. There were 45 more main floor tickets sold than balcony tickets. How many tickets of each kind were sold?

19. Yesterday, four customers at Kay’s Fruit Market bought apples, bananas, cherries, and/or dates. The first customer bought 2 pounds of apples and 1 pound of dates for $4.50. The second customer bought 3 pounds of bananas and 2 pounds of cherries for $9.00. The third customer bought 1 pound of apples, 2 pounds of bananas, and ½ pound of dates for $3.25. And the last customer bought 1 pound of each type fruit

for $7.50. Find the price per pound that Kay charges for each type of fruit.

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20. One night, Glen Rice of the NBA’s Miami Heat scored a total of 35 points against

the Los Angeles Clippers. In professional basketball, it is possible to make 3-point

shots, 2-point shots, and 1-point free-throws. The number of 2-point shots that

Glen made in the game was equal to the sum of the number of 3-point shots he

made and the number of free throws he made. The points that Glen earned from

3-point shots and from free-throws combined was equal to one less than the

number of points he made with 2-point shots. How many of each type of shot did

Glen make in that historic game?

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