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

To solve the proportion \( \frac{5/7}{3/8} = \frac{y}{28/75} \), we can use cross-multiplication.

First, we'll simplify the left side:

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

Now the equation looks like this:

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

Next, we can cross-multiply:

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

Now, let's calculate \( 40 \cdot (28/75) \):

\[ 40 \cdot (28/75) = \frac{40 \cdot 28}{75} = \frac{1120}{75} \]

Thus, we have:

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

Now, we can solve for \( y \):

\[ y = \frac{1120}{75 \cdot 21} = \frac{1120}{1575} \]

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

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

Thus, the solution is:

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