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If 3x = 7y, what are the following ratios?
3y:x

1 Answer

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Final answer:

To find the ratio 3y:x when given the equation 3x = 7y, first solve for y to get y = (3/7)x, then find 3y to be (9/7)x. Simplify this to get the ratio 9:7.

Step-by-step explanation:

You've given the equation 3x = 7y, and you want to find the ratio 3y:x. To do this, first solve the given equation for y in terms of x. Divide both sides of the equation by 7 to get y = (3/7)x. Now, to express 3y in terms of x, multiply both sides by 3 to get 3y = 3*((3/7)x) = (9/7)x. Now you have both y and 3y in terms of x.

The required ratio 3y:x can now be determined. Using the expression for 3y obtained earlier, the ratio is (9/7)x:x. To simplify, divide both the numerator and the denominator by x, because x ≠ 0. You are left with 9/7, which is the simplified form of the ratio. Therefore, the ratio 3y:x is 9:7.

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