Chapter A.8, Problem 22AYU

To determine

To find: A coffee manufacturer wants to market a new blend of coffee that sells for $\text{\$}3.90$ per pound by mixing two coffees that sell for $\text{\$}2.75$ and $\text{\$}5$ per pound, respectively. What amounts of each coffee should be blended to obtain the desired mixture?

Answer to Problem 22AYU

$48.89 \text{lbs}$(amount of $\text{\$}2.75$ coffee in mixture) and $51.11 \text{lbs}$(amount of $\text{\$}5$ coffee in mixture).

Explanation of Solution

A coffee manufacturer wants to market a new blend of coffee that sells for $\text{\$}3.90$ per pound by mixing two coffees that sell for $\text{\$}2.75$ and $\text{\$}5$ per pound, respectively. Assume a total weight of the desired blend is 100 pounds.

Therefore, the equation

$a+b=100\text{lbs}$

That is $2.75a+5b=3.90*100$.

Solving the equation.

To get $a=48.89 \text{lbs}$(amount of $\text{\$}2.75$ coffee in mixture) and $b=51.11 \text{lbs}$(amount of $\text{\$}5$ coffee in mixture).