Chapter 9, Problem 5CLT

To determine

To Find: How many pounds of each type of seed mixture are used to make $200$ pounds of custom bland bird seed costing $\$0.95$ per pound?

Answer to Problem 5CLT

  $120$ Pounds for $\$0.75$ per pound and $80$ pounds for $\$1.75$ per pound.

Explanation of Solution

Given:A custom blend bird is made by mixing two types of bird seeds containing $\$0.75$ per pound and $\$1.75$ per pound.

Let $x$ be the number of pounds of $\$0.75$ and $y$ be the number of pounds of $\$1.75$

Then

The equation becomes

  $\begin{array}{l}x+3y=-1\\ 2x+4y=0\end{array}$

Then

  $\begin{array}{l}\$0.75x+1.25y=200(0.95)\mathrm{...}(i)\\ 0.75x+1.25y=\mathrm{190...}(ii)\end{array}$

Multiply the first equation by $-1.25$

  $\begin{array}{l}-1.25x-1.25y=200(1.95)\\ -1.25x-1.25y=-\mathrm{250....}(iii)\end{array}$

Add equation $(iii)$ and $(ii)$

Then

  $\begin{array}{l}-1.25x-1.25y+0.75x+1.25y=-250+190\\ -0.5x=-60\\ x=120\end{array}$

Substitute $x=120$ in equation $y=200-x$

  $\begin{array}{l}y=200-x\\ y=200-120\\ y=80\\ i.e.\\ x=120\\ y=80\end{array}$

Hence, $120$ pounds for $\$0.75$ per pound and $80$ pounds for $\$1.75$ per pound.