least pludu ut can be carried? one complete sentence, answer the question: How m

Question

least pludu ut can be carried? one complete sentence, answer the question: How many of each 2. Two senators want to study school busing in a particular state an opinion survey using 600 telephone contacts and 400 hous has personnel to do 30 telephone and 10 house contacts pe 20 telephone and 20 house contacts per hour. How many each senator to produce exactly the number of contacts n e contacts. Senator hour, Senator B can handle hours should be scheduled for ee ded? a. Identify the variables of the problem using x and y. b. Fill out the following table from the information given: total telephone contacts house contacts c. Determine the system of equations to be solved. d. Solve the system of equations using Gauss-Jordan Elimination.

Explanation / Answer

2. a. Let the senator A and B work on the study of school busing for x hours and y hours respectively. These are the variables of the problem.

b. Senator A makes 30x telephone contacts and 10x house calls. Also, senator B makes 20y telephone contacts and 20y house calls.    The required table is as under:

x

y

total

telephone contacts

30x

20y

30x+20y

house contacts

10x

20y

10x+20y

c. The system of equations is as under:

30x+20y = 600…(1)

and 10x+20y =400…(2).

d. The augmented matrix of this linear system is A(say)=

30

20

600

10

20

400

  To solve the system, we will reduce A to its RREF as under:

Multiply the 1st row by 1/30

Add -10 times the 1st row to the 2nd row

Multiply the 2nd row by 3/40     

Add -2/3 times the 2nd row to the 1st row

Then the RREF of A is

1

0

10

0

1

15

Thus, x = 10 and y = 15.

x

y

total

telephone contacts

30x

20y

30x+20y

house contacts

10x

20y

10x+20y

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