Given: (5x - 3y)/(5y - 3x) = 3/4

To Find: x:y

Solution:

Cross-multiply:
(5x - 3y) × 4 = (5y - 3x) × 3

Simplify:
20x - 12y = 15y - 9x

Isolate x:
20x + 9x = 15y + 12y
29x = 27y
x/y = 27/29

Therefore, the value of x:y is 27:29.

Explanation:

To solve for x and y, we need to cross-multiply both sides of the given equation. This will eliminate the denominators and give us an equation in terms of x and y.

Once we have the equation, we can simplify it by combining like terms. In this case, we get 20x - 12y = 15y - 9x.

Next, we need to isolate x on one side of the equation. To do this, we can add 9x and 12y to both sides, which gives us 29x = 27y.

Finally, we can find the ratio of x to y by dividing both sides of the equation by y. This gives us x/y = 27/29. Therefore, the value of x:y is 27:29.

Conclusion:

The ratio of x to y is 27:29.