$$\frac{3a}{5}=\frac{3b}{2}$$
$a=\frac{5b}{2}$
$$2\times 3a=5\times 3b$$
$$6a=5\times 3b$$
$$6a=15b$$
$$\frac{6a}{6}=\frac{15b}{6}$$
$$a=\frac{15b}{6}$$
$$a=\frac{5b}{2}$$
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$b=\frac{2a}{5}$
$$15b=6a$$
$$\frac{15b}{15}=\frac{6a}{15}$$
$$b=\frac{6a}{15}$$
$$b=\frac{2a}{5}$$