Question

How many oz of walnuts which cost $6/oz must be added to 2 oz of peanuts which cost $12/oz to make mixed nuts which cost $8/oz

Answer 1

Answer:  4 oz

Step-by-step explanation:

Create a table.  Multiply across and add down (the middle column cannot be added).  The Mixture line creates the equation that must be solved.

Let x represent the unknown quantity of walnuts.

$\begin{array}{c|c|c||c}&\underline{Quantity}&\underline{Cost}&\underline{Qty \times Cost}\\Walnuts&x&6&6x\\\underline{Peanuts}&\underline{\qquad 2\qquad}&\underline{\qquad 12\qquad}&\underline{\qquad 24\qquad }\\Mixture&x+2&8&6x+24\end{array}$

$.\qquad \qquad \qquad \qquad (x+2)(8) = 6x+24\\.\qquad \qquad \qquad \qquad 8x + 16 = 6x + 24\longrightarrow \text{distributed}\\.\qquad \qquad \qquad \qquad2x+16=24\qquad \longrightarrow \text{subtracted 6x}\\.\qquad \qquad \qquad \qquad 2x=8\qquad \qquad \ \longrightarrow \text{subtracted 16}\\.\qquad \qquad \qquad \qquad x=4\qquad \qquad \quad \longrightarrow \text{divided by 2}$