"at this rate", well, we're assuming the rate for the apples is the same as the rate for the bananas, so we'd be assuming that 3⅝ lbs of bananas cost $6.85.
let's first convert the 3⅝ to an improper fraction.
[tex]\bf \stackrel{mixed}{3\frac{5}{8}}\implies \cfrac{3\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{29}{8}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} lbs&\$\\ \cline{1-2}\\ \frac{29}{8}&6.85\\\\ 5.25&x \end{array}\implies \cfrac{~~\frac{29}{8} ~~}{5.25}=\cfrac{6.85}{x}\implies \cfrac{29}{8}x=(5.25)(6.85) \\\\\\ \cfrac{29x}{8}=35.9625\implies 29x=8(35.9625)\implies 29x=287.7 \\\\\\ x = \cfrac{287.7}{29}\implies x\approx 9.92[/tex]
