Chapter 9, Problem 5CLT

To determine

To find:The pounds of each seed mixture to obtain 200 pounds of custom-blend bird seed costing 0.95 dollars per pound.

Answer to Problem 5CLT

To obtain the required mixture, 120 pounds of mixture costing 0.75 dollars per pound and 80 pounds of mixture costing 1.25 dollars per pound is used.

Explanation of Solution

Given:

The two types of seeds mixtures are 0.75 dollars per pound and 1.25 dollars per pound.

The required mixture is 200 pounds costing 0.95 dollars per pound.

Calculation:

Let $x$ and $y$ represent the pounds of 0.75 dollars per pound and 1.25 dollars per pound of seed mixture, respectively.

Based on the giveninformation, following two equations are obtained:

  $x+y=200$  ...(1)

  $\begin{array}{c}0.75x+1.25y=200\times 0.95\\ 0.75x+1.25y=190\end{array}$  ...(2)

By the method of elimination for solving a system, first multiply equation (1) by -1.25 and add to equation (2), as shown below:

  $\begin{array}{c}0.75x+1.25y-1.25\left(x+y\right)=190-\left(190\times 1.25\right)\\ 0.75x+1.25y-1.25x-1.25y=-60\\ -0.50x=-60\\ x=120\end{array}$  ...(3)

Substitute the value of $x$ from (3) in equation (1) to obtain the value of $y$ .

  $\begin{array}{c}120+y=200\\ y=80\end{array}$

So, 120 pounds of mixture costing 0.75 dollars per pound and 80 pounds of mixture costing 1.25 dollars per pound is used to obtain the required mixture.