Answer
$\text{22.5 pounds of cashews, and 52.5 pounds of of the whole mixture.}$
Work Step by Step
Let us consider that $\text{x= Number of pounds of cashews and}$ $\text{y =Number of pounds of the whole mixture}$
We are given:
$x+30=y~~~(1) $
and
$5x+1.5(30)=3y~~~(2)$
We substitute equation (1) into equation (2):
$5x+1.5(30)=3(x+30)\\
5x+45=3x+90\\
2x=45\\
x=22.5 \ pounds$
Now, back substitute the value of $x$ into Equation (1) to solve for $y$:
$22.5+30=y \implies y=52.5$
Therefore, our desired results are:
$\text{22.5 pounds of cashews, and 52.5 pounds of of the whole mixture.}$
