Chapter 4, Problem 29RE

### 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

# Purchasing You are the buyer for OHaganBooks.com and are considering increasing stocks of romance and horror novels at the new OHaganBooks.com warehouse in Texas. You have offers from two publishers: Duffin House and Higgins Press. Duffin offers a package of 5 horror novels and 5 romance novels for $50, and Higgins offers a package of 5 horror and 11 romance novels for$150. Exercises 29–32 give different scenarios for your purchasing options in response to these offers.How many packages should you purchase from each publisher to get exactly 4,500 horror novels and 6,600 romance novels?

To determine

To calculate: The number of packages that should be purchased from Duffin House and Higgins Press publishers to get exactly 4,500 horror novels and 6,600 romance novels.

Explanation

Given Information:

A buyer for OHagenBook.com consider to increase stocks of romance and horror novels at the new OHagenBook.com warehouse in Texas. He receives an offer from two publishers: Duffin house and Higgins Press. Duffin offers a package of 5 horror novels and 5 romance novels for $50 whereas Higgins offers a package of 5 horror and 11 romance novels for$150.

He wants to get exactly 4,500 horror novels and 6,600 romance novels.

Formula Used:

Elimination method:

In this method, first, combine the equations in a way such that one of the variables gets eliminated. Then substitute the value obtained of one variable in either of the equation to get the value of the other variable.

Calculation:

Let x be the number of packages in Duffin house and y be the number of packages in Higgins press.

Next, organize the given information in a table,

 Duffin (x) Higgins (y) Required Totals Horror 5 5 4500 Romance 5 11 6600

Now, the required totals of horror and romance categories in the table formed will result in two linear equations:

5x+5y=45005x+11y=6600

Apply the elimination method to find the solution of the given system of the equations:

Multiply the first equation by ā1 and rewrite the equations, such that the coefficient of x in both the equations is equal but with opposite sign:

ā5xā5

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