Chapter 4, Problem 37RE

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# Website Traffic OHaganBooks.com has two principal competitors: JungleBooks.com and FarmerBooks.com. Combined website traffic at the three sites is estimated at 10,000 hits per day. Only 10% of the hits at OHaganBooks.com result in orders, whereas JungleBooks.com and FarmerBooks.com report that 20% of the hits at their sites result in book orders. Together, the three sites process 1,500 book orders per day. FarmerBooks.com appears to be the most successful of the three and gets as many book orders as the other two combined. What is the traffic (in hits per day) at each of the sites?

To determine

To calculate: The amount of traffic at each of the sites.

Explanation

Given Information:

JungleBooks.com and FarmerBooks.com are the two principal competitors OHaganBooks.com. Combined traffic of three sites is 10,000 hits per day. 10% of hits at OHaganBooks.com brings orders, while the JungleBooks.com and FarmerBooks.com report that 20% of the hits at their sites result in book orders. Together 1500 book orders are processed per day by the three sites. FarmerBooks.com gets as many book orders as the other two sites get combined.

Formula Used:

Elementary row operations:

Type 1: Replacing the row Ri by aRi, where a is a nonzero number.

Type 2: Replacing the row Ri by aRiĀ±bRj, where a is a nonzero number.

Gauss Jordan reduction method:

Step 1: First clear the fractions or decimals if any.

Step 2: Pivot the first nonzero element of the first row.

Step 3: Use the pivot to clear its column.

Step 4: Pivot the first nonzero element in the second row and clear the column.

Step 5: Pivot the first nonzero element in the third row and clear the column.

Step 6: Turn all the pivot elements into a 1.

Calculation:

Firstly identify and label the unknowns.

Considering the provided information the unknowns should be labelled like this,

x= The number of hits at OHaganBooks.com

y= The number of hits at JungleBooks.com

z= The number of hits at FarmerBooks.com

Now, we are provided that combined traffic of the three sites is estimated to be 10,000 hits per day which can be represented as,

x+y+z=10000

From the information provided we know that the three sites brings a total 1500 orders in a day, where only 10% hits of OHaganBooks.com results in orders, while the JungleBooks.com and FarmerBooks.com get 20% of their hits as book orders. This can be written in the form of equation as,

0.1x+0.2y+0.2z=1500

Also, the FarmerBooks.com brings the same amount of orders as the other two sites combined.

0.2z=0.1x+0.2y0.1x+0.2yā0.2z=0

The augmented matrix for the obtained equations is:

[111100000.10.20.215000.10.2ā0.20]

Apply Gauss Jordan reduction method to get the solution of the given system of equation.

Begin by clearing the fraction in the rows of the matrix by the operation R2ā10R2,R3ā10R3

[111100000.10.20.215000.10.2ā0.20]ā[111100001221500012ā20]

Now, pivot the first nonzero element of first row and clear its column

Perform the operation R2āR2āR1,R3āR3āR1,

[111100001221500012ā20]ā[11110000011500001ā3ā10000]

Now, pivot the first nonzero element of second row and clear its column

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