Final answer:
The ratio of x to y given the equation 6x=7y is found by dividing both sides by 6 and then y, resulting in the ratio 7:6.
Step-by-step explanation:
To find the ratio of x to y given the equation 6x=7y, we need to manipulate the equation to isolate the variables in a way that allows us to compare them directly. We begin by dividing both sides of the equation by 6 to solve for x in terms of y, which gives us x=(7/6)y. Once this is achieved, we divide both sides of this new expression by y to get x/y = 7/6, thus the ratio of x to y is 7:6.
To find the ratio x:y, we can rearrange the given equation 6x = 7y to solve for x in terms of y. Divide both sides of the equation by 6 to isolate x. We get x = (7/6)y. Now we can express the ratio x:y by dividing both sides of the equation by y. This gives us (7/6)y : y as the ratio.
Simplifying further, we can cancel out the y terms to get the final ratio 7:6.
Therefore, the ratio x:y is 7:6.