Question

At a gourmet nut shop, nuts are sold in bulk. Cashews sell for $1.40 per pound and macadamia nuts sell for $8.55 per pound. Lee wishes to purchase 5 pounds of mixed nuts by mixing 3.5 pounds of cashews and 1.5 pounds of macadamia nuts. What will be the price per pound of the mixture?

Answer 1

`\bf \begin{array}{rrcccllll} &lbs&(\$)/(lb)&total\ \$\\ &-----&-----&-----\\ cashew&3.5&1.4&(3.5)(1.4)\\ macadamia&+1.5&8.55&(1.5)(8.55)\\ -----&-----&-----&-----\\ mixture&5&x&(5)(x) \end{array}\\\\ -----------------------------\\\\ \textit{thus, the price for lb for the mixture is} \\\\ 5x=(3.5)(1.4)+(1.5)(8.55)\implies x=\cfrac{(3.5)(1.4)+(1.5)(8.55)}{5}`