Question

A coffee Merchant combines coffee costing $6 per pound with coffee costing $3.50 per pound how many pounds of each should be used to make a 25 lb of a blend costing $5.25 per pound

Answer 1

$\bf \begin{array}{lccclll} &\stackrel{lb}{amount}&\stackrel{lb}{price}&\stackrel{total}{price}\\ &------&------&------\\ \textit{6 per lb coffee}&x&6&6x\\ \textit{3.5 per lb coffee}&y&3.5&3.5y\\ -------&------&------&------\\ mixture&25&5.25&131.25 \end{array}$

same as before, we add the 1st and 3rd columns, since the mixture is just the sum of the elements above it.

$\bf \begin{cases} x+y=25\implies \boxed{y}=25-x\\ 6x+3.5y=131.25\\ ----------\\ 6x+3.5\left( \boxed{25-x} \right)=131.25 \end{cases} \\\\\\ 6x+87.5-3.5x=131.25\implies 2.5x=131.25-87.5 \\\\\\ 2.5x=43.75\implies x=\cfrac{43.75}{2.5}\implies x=17.5$

how many lbs will it be of the 3.50 per lb coffee?  well, y = 25 -x.