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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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Chapter
Section
BuyFindarrow_forward

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.

You want to spend a total of $50,000 on books and have promised to buy twice as many packages from Duffin as from Higgins. How many packages should you purchase from each publisher?

To determine

To calculate: The number of packages that should be purchased from each publisher if the total money spends on books is $50,000 and also have to buy twice as many novels from Duffin as from Higgins.

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 spend a total of $50,000 on books and also have to buy twice as many novels from Duffin as from Higgins.

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 buy from Duffin house and y be the number of packages buy from Higgins press.

Equate the total cost expression to the required total cost to get the cost equation,

50x+150y=50000 …… (1)

Now, consider the given information that it is promised to buy twice as many as from Duffin as from Higgins to form the second equation.

x=2y

Rewrite the equation in standard form to get,

x2y=0 …… (2)

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

Divide the equation (1) by 50

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