Question

Given the following application problem, solve it using the steps 1--5:

1) Declare the variables

2) Set up a table with rows and columns corresponding to the different quantities talked about

3) Write a system of equations whose solution will provide the answer to the question asked

4) Solve it using a matrix.

5) Interpret your solution.

An art teacher finds that colored paper can be bought in three different packages. The first
package has 20 sheets of white paper, 15 sheets of blue paper, and 1 sheet of red paper. The
second package has 3 sheets of blue paper and 1 sheet of red paper. The last package has 2
sheets of red paper. The teacher needs a total of 200 sheets of white paper, 180 sheets of blue
paper, and 22 sheets of red paper. How many of each type of package should he order so that
he does not have any paper left over?

Answer 1

(1) Let the no. of each type of package ordered be P1, P2, P3.

(2)

Sheet colour	P1	P2	P3	Total no. of pages of each colour
white	20	0	0	200
blue	15	3	0	180
red	1	1	2	22

(3) System of equations is as follows:

20P1 = 200

15P1 + 3P2 = 180

P1 + P2 + P3 = 22

(4) In matrix form, it can be written as

or AP=B

To calculate P P =

P1 = 10, P2 = 10 , P3 =1 Ans

(5) The no. of first type of packages required is 10.

The no. of second type of packages required is 10.

The no. of last type of packages required is 1.