Question

A nut mixture consists of almonds and cashews. almonds are $3.75 per pound and cashews $6.72 per pound. how many pounds of each type of nut should be mixed to produce 10 lb selling for $5.22 per pound​

Answer 1

Answer: 5 lbs each

Step-by-step explanation:

Create a table such that you multiply across and add down (first and last column only). Then solve the equation that develops in the last row.

$\begin{array}{l|c|c||l}&\underline{Qty(lbs)}&\underline{Price(\ )}&\underline{\qquad Price \times Qty\qquad}\\Almonds&x&3.75&\qquad 3.75(x)=3.75x\\\underline{Cashews}&\underline{10-x}&\underline{6.72}&\underline{6.72(10-x)=67.2-6.72x}\\Mixture&10&5.22&\qquad 3.75x+67.2-6.72x\end{array}\\\\\\.\qquad \qquad \qquad \qquad 5.22(10)=3.75x+67.2-6.72x\\.\qquad \qquad \qquad \qquad \qquad 52.2 =-2.97x+67.2\\.\qquad \qquad \qquad \qquad \quad -15.0=-2.97x\\.\qquad \qquad \qquad \qquad \qquad \ 5.0=x$

If x = 5,

then 10 - x = 10 - 5 = 5