Answer
$23\frac{1}{3}$ pounds of cashews and $11\frac{2}{3}$ pounds of walnuts.
Work Step by Step
Step 1. Assume the owner needs $x$ pounds of cashews and $y$ pounds of walnuts, we have $x+y=35$ which gives $y=35-x$
Step 2. The total value is given by $7x+5.5y=6.5(35)=227.5$
Step 3. Substitute the relation in Step-1 in the equation of Step-2, we have $7x+5.5(35-x)=227.5$ which gives $7x+192.5-5.5x=227.5\longrightarrow 1.5x=35$, thus $x=\frac{35}{1.5}=\frac{70}{3}=23\frac{1}{3}\ lb$ and $y=35-x=11\frac{2}{3}\ lb$
Step 4. The owner needs $23\frac{1}{3}$ pounds of cashews and $11\frac{2}{3}$ pounds of walnuts.
