GIVEN: $\frac{3x}{2}=\frac{5}{7y}$

Cross multiply to get: $(3x)(7y) = (2)(5)$

Simplify: $21xy = 20$

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GIVEN: $\frac{3y}{5}=\frac{a}{x}$

Cross multiply to get: $(x)(3y) = (5)(a)$

Simplify: $3xy =5a$

Multiply both sides by 7 to get: $21xy =35a$

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At this point we know the following:
$21xy = 20$
$21xy =35a$

Since both equations are set equal to $21xy$, we can conclude that: $35a =10$

Divide both sides by 35 to get: $a = \frac{10}{35} = \frac{2}{7}$

Answer: $\frac{2}{7}$

Cheers,
Brent