B Apply

30. Business A manufacturer sells pencils and erasers in packages. The price of a package of five erasers and two pencils is $.23. The price of a package of seven erasers and five pencils is $.41. Write a system of equations to represent this situation. Then write a matrix to represent the system.
31. Think About a Plan Last year your town invested a total of $25,000 into two separate funds. The return on one fund was 4% and the return on the other was 6%. If the town earned a total of $1300 in interest, how much money was invested in each fund?
    • What variables will you use? What will they represent?
    • What equations can you write to model this situation?
    • How can you use a matrix to solve this system?

Graphing Calculator Solve each system.

32. { x + y + z = 2   2 y − 2 z = 2 x − 3 z = 1 left brace . table with 3 rows and 4 columns , row1 column 1 , x plus , column 2 y plus , column 3 z equals , column 4 2 , row2 column 1 , , column 2 2 y minus , column 3 2 z equals , column 4 2 , row3 column 1 , x , column 2 minus , column 3 3 z equals , column 4 1 , end table
33. { x − y + z = 3 x + 3 z = 6   y − 2 z = − 1 left brace . table with 3 rows and 4 columns , row1 column 1 , x minus , column 2 y plus , column 3 z equals , column 4 3 , row2 column 1 , x , column 2 plus , column 3 3 z equals , column 4 6 , row3 column 1 , , column 2 y minus , column 3 2 z equals , column 4 negative 1 , end table
34. { x + y + z = − 1 3 x + 4 y − z = 8 6 x + 8 y − 2 z = 16 left brace . table with 3 rows and 4 columns , row1 column 1 , x plus , column 2 y plus , column 3 z equals , column 4 negative 1 , row2 column 1 , 3 x plus , column 2 4 y minus , column 3 z equals , column 4 8 , row3 column 1 , 6 x plus , column 2 8 y minus , column 3 2 z equals , column 4 16 , end table
35. { x − y + 3 z = 9 x + 2 z = 3 2 x + 2 y + z = 10 left brace . table with 3 rows and 4 columns , row1 column 1 , x minus , column 2 y plus , column 3 3 z equals , column 4 9 , row2 column 1 , x , column 2 plus , column 3 2 z equals , column 4 3 , row3 column 1 , 2 x plus , column 2 2 y plus , column 3 z equals , column 4 10 , end table
36. { 2 x + 3 y + z = 13 5 x − 2 y − 4 z = 7 4 x + 5 y + 3 z = 25 left brace . table with 3 rows and 4 columns , row1 column 1 , 2 x plus , column 2 3 y plus , column 3 z equals , column 4 13 , row2 column 1 , 5 x minus , column 2 2 y minus , column 3 4 z equals , column 4 7 , row3 column 1 , 4 x plus , column 2 5 y plus , column 3 3 z equals , column 4 25 , end table
37. { − 2 w + x + y   = 0 − w + 2 x − y + z = 1 − 2 w + 3 x + 3 y + 2 z = 6 w + x + 2 y + z = 5 left brace . table with 4 rows and 6 columns , row1 column 1 , negative 2 w plus , column 2 x plus , column 3 y , column 4 , column 5 equals , column 6 0 , row2 column 1 , negative w plus , column 2 2 x minus , column 3 y , column 4 plus , column 5 z equals , column 6 1 , row3 column 1 , negative 2 w plus , column 2 3 x plus , column 3 3 y , column 4 plus , column 5 2 z equals , column 6 6 , row4 column 1 , w plus , column 2 x plus , column 3 2 y , column 4 plus , column 5 z equals , column 6 5 , end table

38. Snacks Suppose you want to fill nine 1-lb tins with a snack mix. You have $15 and plan to buy almonds for $2.45 per lb, hazelnuts for $1.85 per lb, and raisins for $.80 per lb. You want the mix to contain an equal amount of almonds and hazelnuts and twice as much of the nuts as the raisins by weight.

    1. Writing Explain how each equation below relates to the problem. What does each variable represent?

       { x + y + z = 9 2.45 x + 1.85 y + 0.85 z = 15 x + y = 2 z left brace . table with 3 rows and 1 column , row1 column 1 , x plus y plus z equals 9 , row2 column 1 , 2.45 , x plus , 1.85 , y plus , 0.85 , z equals 15 , row3 column 1 , x plus y equals 2 z , end table

    2. Solve the system.
    3. How many of each ingredient should you buy?
39. Geometry The coordinates (x, y) of a point in a plane are the solution of the system { 2 x + 3 y = 13 5 x + 7 y = 31 . left brace . table with 2 rows and 3 columns , row1 column 1 , 2 x plus , column 2 3 y equals , column 3 13 , row2 column 1 , 5 x plus , column 2 7 y equals , column 3 31 , end table . .  Find the coordinates of the point.

40. Error Analysis A classmate writes the matrix below to represent a system and says that the solution is x = 2, y = 0. Explain your classmate's error and describe how to correct it.

    
    Image Long Description

41. Paint A hardware store mixes paints in a ratio of two parts red to six parts yellow to make two gallons of pumpkin orange. A ratio of five parts red to three parts yellow makes two gallons of pepper red. A gallon of pumpkin orange sells for $25, and a gallon of pepper red sells for $28. Find the cost of 1 quart of red paint and the cost of 1 quart of yellow paint.

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