Question

How many pounds of walnuts, which cost $3 per pound, must be mixed with 30 pounds ofalmonds costing $8.25 per pound to make a mixture which will cost $6.50 per pound?

Answer 1

Let w be the number of pounds of walnuts . Then, we can write

$3w+30(8.25)=(w+30)(6.25)$

because the mixture (w+30) will cost $6.25 per pound. This equation can be written as

$3w+247.5=6.25w+187.5$

then, by moving 187.5 to the left hand side and 3w to the right hand side, we get

$247.5-187.5=6.25w-3w$

which gives

$\begin{gathered} \text{ 60=3.25w} \\ \text{then } \\ w=\frac{60}{3.25} \\ w=18.46 \end{gathered}$

this means that we must mix 18.46 pounds of walnuts with 30 pounds of almonds which will costs $6.50 per pound