5/7:3/8=y:28/75

To solve the proportion \(\frac{5/7}{3/8} = \frac{y}{28/75}\), we'll first simplify the left side and then solve for \(y\).

Starting with the left side, we have:

\[ \frac{5/7}{3/8} = \frac{5}{7} \times \frac{8}{3} = \frac{5 \times 8}{7 \times 3} = \frac{40}{21} \]

Now the proportion can be rewritten as:

\[ \frac{40}{21} = \frac{y}{28/75} \]

Next, we can cross-multiply to solve for \(y\):

\[ 40 \times (28/75) = 21 \times y \]

Calculating \(40 \times \frac{28}{75}\):

\[ 40 \times \frac{28}{75} = \frac{40 \times 28}{75} = \frac{1120}{75} \]

Now substituting back into the equation gives us:

\[ \frac{1120}{75} = 21y \]

To isolate \(y\), we divide both sides by 21:

\[ y = \frac{1120}{75 \times 21} \]

Calculating \(75 \times 21\):

\[ 75 \times 21 = 1575 \]

Thus, we have:

\[ y = \frac{1120}{1575} \]

To simplify \(\frac{1120}{1575}\), we can divide both numerator and denominator by their greatest common divisor (GCD). The GCD of 1120 and 1575 is 5:

\[ y = \frac{1120 \div 5}{1575 \div 5} = \frac{224}{315} \]

So the final value of \(y\) is:

\[ \boxed{\frac{224}{315}} \]