$\textbf{Answer:}$

$\frac{3}{2}$

$\textbf{Explaination:}$

$\frac{a}{b} = \frac{3}{4}$

$ \implies a = \frac{3}{4} b $ . . .(1)

and $ 8a +5b=22$ . . .(2)

Substitute (1) into (2), we have

$ 8 \left( \frac{3}{4}b \right) +5b = 22$

$ \frac{24}{4} b+5b=22$

$6b+5b=22$

$11b =22$

$b=2$ . . . (3)

substitute (3) into (1), we get

$a = \frac{3}{4}(2)$

$a = \frac{3}{2}$