Chapter 4, Problem 37RE

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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.

**Formula Used:**

Elementary row operations:

Type 1: Replacing the row

Type 2: Replacing the row

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,

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,

From the information provided we know that the three sites brings a total 1500 orders in a day, where only

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

The augmented matrix for the obtained equations is:

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

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

Perform the operation

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

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