4.5 Solving Systems of Equations using Inverse Matrices
INSTRUCTIONS:
Set-up equations for all problems and check with Mr. Bergmann to make sure they are correct. Then, convert your equations to matrices, and use inverse matrices to complete all problems.
Use your calculator to find you’re A-1 matrix and multiply it by B .
1.In 1960, Paul Hornung (of the Green Bay Packers), set a NFL record when he scored 176 points in one season. Those points came from a combination of 6-point Touchdowns, 1-point Extra Points, and 3-point Field Goals. Hornung scored a total of 71 times, and his number of Extra Points were 11 more than his Touchdowns and Field Goals combined. How many of each type of score did Hornung have?
2. The UW-Madison band is organizing a trip to a national competition for the 226-member marching band. A bus will hold 70 students and their instruments. A van will hold 8 students and their instruments. A bus costs $280 to rent for the trip. A van costs $70 to rent for the trip. The band has $980 to use for the transportation. How many busses and vans should the band take?
3. Jean, Ray, and Henry go to a Chinese restaurant for lunch and order three different combination platters. Jean orders 2 portions of fried rice and 1 portion of chicken chow mein. Ray orders 1 portion of fried rice, 1 portion of chicken chow mein, and 1 portion of sautéed broccoli. Henry orders 1 portion of sautéed broccoli and 2 portions of chicken chow mein. Jean’s platter costs $5, Ray’s costs $5.25, and Henry’s costs $5.75. How much does each entrée cost?
4.Colders is having a Christmas sale. You can purchase a Sofa and a Love Seat for $1300. A Sofa and 2 Chairs costs $1400. Or, you can get a Sofa, a Love Seat, and a Chair for $1600. How much does each piece of furniture cost individually?
5. Meg and Jake share the driving on a 280 mile trip. Meg’s average speed was 58 miles per hour. Jake’s average speed was 53 miles per hour. Meg drove one hour longer than Jake did. How many hours did they each drive?
6. You have $25 to spend on picking 21 pounds of three different types of apples in an orchard. The Empire apples cost $1.40 per pound, the Red Delicious apples cost $1.10 per pound, and the Golden Delicious apples cost $1.30 per pound. You want twice as many Red Delicious apples as the other two kinds combined. How many pounds of each type of apple should you buy?
7. Selling frozen yogurt at a fair, you make $565 and use 250 cones. A single-scoop cone costs $2 and a double-scoop cone costs $2.50. How many of each type of cone did you sell?