Chapter 8.2, Problem 67STP

To determine

To find: The number of pounds of cheddar cheese received by both booths.

Answer to Problem 67STP

The booth 1 has $190\text{lbs}$ , booth 2 has $150\text{lbs}$ , and booth 3 has $100\text{lbs}$ .

Explanation of Solution

Given:

The given table is as follows.

Type	Booth 1	Booth 2	Booth 3
Cheddar	$40\%$	$30\%$	$10\%$
Monterey Jack	$40\%$	$90\%$	$80\%$
Swiss	$30\%$	$70\%$	$70\%$

Calculation:

Booth 1 received $x$ pound of cheese each morning.

Booth 2 received $y$ pound of cheese each morning.

Booth 3 received $z$ pound of cheese each morning.

Write the equations.

  $\begin{array}{c}\text{Cheddar}=0.4x+0.3y+0.1z\\ 0.4x+0.3y+0.1z=131\dots \left(1\right)\\ \text{Monterey}\text{Jack}=0.4x+0.9y+0.8z\\ 0.4x+0.9y+0.8z=291\dots \left(2\right)\end{array}$

And,

  $\begin{array}{c}\text{Swiss}=0.3x+0.7y+0.7z\\ 0.3x+0.7y+0.7z=232\dots \left(3\right)\end{array}$

Solve the equations (1), (2), and (3).

  $\begin{array}{c}x=190\\ y=15\\ z=100\end{array}$

Therefore, the booth 1 has $190\text{lbs}$ , booth 2 has $150\text{lbs}$ , and booth 3 has $100\text{lbs}$ .