When will I actually USE this math



[pic] When will I actually USE this math??!!

Use matrices to solve the following problems. Use a highlighter to highlight important information; name your variables; set up your equations; set up your matrix equations; use your calculator to solve. Show all work on a separate sheet of paper. BE SURE TO ANSWER THE QUESTION!!

1. You are selling tickets at a high school football game. Student tickets cost $2 and general admission tickets cost $3. You sell 1957 tickets and collect $5035. How many of each type of ticket did you sell?

2. Your teacher is giving a test worth 150 points. There are 46 three- and five-point questions. How many of each are on the test?

3. A small furniture company manufactures sofas and recliners. Each sofa requires 8 hours of labor and $60 in materials, while a recliner can be built for $35 in 6 hours. The company has 340 hours of labor available each week and can afford to buy $2250 worth of materials. How many recliners and sofas can be produced if all labor hours and all materials must be used?

4. Two investments are made totaling $23,000. For a certain year these investments yield $2095 in simple interest. Part of the $23,000 is invested at 8% and the rest at 11%. How much is invested at each rate?

5. Gene works at the China Emporium on Saturday packing dishes for shipment. He received $.12 for each piece he packs successfully, and he is fined .18 for each piece he breaks. If he handles 188 pieces and is paid $20.16, how many pieces did he break?

6. A collection of nickels and dimes is worth $3.30. There are 42 coins in all. How many of each coin are there?

7. Sue has $21.40 in dimes and quarters for a total of 100 coins. How many of each kind of coin does she have?

8. The perimeter of a lot is 84 feet. The length exceeds the width by 16 feet. Find the length and the width of the lot.

9. A dorm room at a college your sister is considering seems small. The room is rectangular and has a perimeter of 42 feet. The room is 4 feet longer than it is wide. What are the dimensions of the room?

10. Patrick is 4 years younger than his sister Alice. In five years, Patrick will be [pic]as old as Alice. How old is Patrick now?

11. Five hundred tickets were sold for a certain music concert. The tickets for the adults sold for $7.50, the tickets for the children sold for $4.00, and tickets for senior citizen sold for $3.50. The revenue for the Monday performance was $3,025. Twice as many adult tickets were sold as children tickets. How many of each ticket was sold?

12. At a college production of Evita, 400 tickets were sold. The ticket prices were $8, $10, $12, and the total income from ticket sales was $3700. How many tickets of each type were sold if the combined number of $8 and $10 tickets sold was 7 times the number of $12 tickets sold?

13. A dietician wishes a patient to have a meal that has 66 grams of protein, 94.5 grams of carbohydrates, and 910 milligrams of calcium. The hospital food service tells the dietician that the dinner for today is chicken, corn, and 2% milk. Each serving of chicken has 30 grams of protein, 35 grams of carbohydrates, and 200 milligrams of calcium. Each serving of corn has 3 grams of protein, 16 grams of carbohydrates, and 10 milligrams of calcium. Each glass of 2% milk has 9 grams of protein, 13 grams of carbohydrates, and 300 mg of calcium. How many serving of each food should the dietician provide for the patient?

14. A Broadway theater has 500 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $50, main seats for $35, and balcony seats for $25. If all the seats are sold, the gross revenue to the theater is $17,100. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $14,600. How many are there of each kind of seat?

15. The 2002 Winter Olympics were held in Salt Lake City, Utah. The planned budget for this event was $1162 million. This included three categories: operating expenses, facilities construction, and surplus. The amount allowed for operating expenses was the same as the total allowed for facilities construction and surplus combined. The budget committee estimated that 14% of the toal budget would be surplus. How much money was budgeted for each area?

16. The 1991 gross state product of North Carolina can be classified into three categories: services, agriculture, and industrial goods. The total state gross product was $35 billion. Services and agriculture combined made up six sevenths of the gross state product. Services produced find and one fifth times as much as industry. What was the value of services, agricultural products, and industrial goods in 1991?

17. A nursery receives a shipment of 246 trees. The shipment includes pine trees, fruit trees, and maple trees. There are twice as many pine trees as there are fruit trees. The maple trees make up half of the shipment. How many of each type of tree was in this shipment?

18. In 1998, there were 6.047 million people registered to vote in Florida. Of these, d million were democrats, r million were republicans, and I million were independent. There were .908 million more democrats than republicans, and there were 1.935 million more republicans than independent voters. How many people are registered in each party?

|Stock |Expected Return |

|IBM |6% |

|Disney |8% |

|AOL |12% |

19. You have $10,000 to invest tin three types of stock. The expected annual returns for the three stocks are shown in the table below. You want the combined investment in IBM and Disney to be three times the amount invested in AOL. You are hoping to obtain an average return of 8.5%. How much should you invest in each stock?

20. Alexandria High School scored 37 points in a football game. Six points are awarded for each touchdown. After each touchdown, the team can earn one point for the extra kick or two points for a 2-point conversion. The team scored one fewer 2-points conversions than extra kicks. The team scored 10 times during the game. How many touchdowns were made during the game?

21. Three solutions contain a certain acid. The first contains 10% acid, the second 30%, and the third 50%. A chemist wishes to use all three solutions to obtain a 50 – liter mixture containing 32% acid. If the chemist wants to use twice as much of the 50% solution as the 30% solution, how many liters of each solution should be used?

Solve the following problems by graphing to find the solution.

22. One car model costs $12000 and costs an average of $0.30 per mile to maintain. Another car model costs $14000 and costs an average of $0.20 per mile to maintain. If one of each model is driven the same number of miles, after how many miles would the total cost of one model be the same as the other? If you were to put 50,000 miles on the car, which car should you buy?

23. For 1987-1994, the per capita incomes in Nevada and New Hampshire can be modeled by:

N = 1007t + 9035

H = 712t + 13,324

(t = 7 represents 1987). Approximate the year in which per capita income in Nevada surpassed in New Hampshire.

24. You and your friends are going to produce and record a CD. It costs $400 to rent a studio and $4 per CD that you produce. You are planning on selling the CD’s for $8 each. How many CD’s will you have to sell in order to make a profit?

25. A rental car agency charges $18 per day plus 13 cents per mile to rent a certain car. Another agency charges $23 per day plus 9 cents per mile to rent the same car. How many miles per day will have to be driven for the cost of a car from the first agency to equal the cost of a car from the second agency?

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