Chapter 4.3, Problem 9E

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7th Edition

Stefan Waner + 1 other

ISBN: 9781337274203

Textbook Problem

**Supply** A bagel store orders cream cheese from three suppliers: Cheesy Cream Crop. (CCC), *Super Smooth & Sons* (SSS), and *Bagel’s Best Friend Co*. (BBF). One month, the total order of cheese came to 100 tons. (The store does do a booming trade.) The costs were $80, $50, and $65 per ton from the three suppliers, respectively, with total cost amounting to $5,990. Given that the store ordered the same amount from CCC and BBF, how many tons of cream cheese were ordered from each supplier?

To determine

**To calculate:** The tons of cream cheese ordered from each supplier. It is observed that the total order of cheese came to 100 tons. Also, the costs of cream cheese per ton from supplier CCC was $80, from supplier SSS was $50 and from the supplier, BBF was $65, with total cost amounting to $5990. The order amount was the same from suppliers CCC and BBF.

Explanation

**Given Information:**

The total order of cheese came to 100 tons.

Also, the costs of cream cheese per ton from supplier CCC was $80, from supplier SSS was $50 and from the supplier, BBF was $65, with total cost amounting to $5990. The order amount was the same from suppliers CCC and BBF.

**Formula Used:**

Elimination method:

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

**Calculation:**

Let the amount of cream cheese from each supplier be denoted by variables

Thus,

*x* is tons of cream cheese supplied by CCC.

*y* is tons of cream cheese supplied by SSS.

*z* is tons of cream cheese supplied by BBF.

The given data shows that the total order of cheese came to 100 tons.

Thus, we can say that:

The condition says that the order amount was the same from suppliers CCC and BBF.

Thus,

And according to the cost of cheese from each supplier and the total amount is $5990.

Thus,

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

Begin by multiplying the first equation with 50 and subtracting it from third to eliminate *y.*

Replace the variables in equation (1) using (2) and (3)

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