Great question!

GIVEN: The ratio of \(x\) to \(y\) is \(4\) to \(7\)

In other words: \(\frac{x}{y} = \frac{4}{7}\)

Cross multiply to get: \(7x=4y\)

Divide both sides by 4 to get: \(\frac{7x}{4} = y\)

At this point we can replace \(y\) with \(\frac{7x}{4}\) in the original comparison to get:

Quantity A: \( \frac{7x}{4} - x\)

Quantity B: \(3\)


Rewrite Quantity A as follows:
Quantity A: \(\frac{7x}{4} - \frac{4x}{4}\)

Quantity B: \(3\)


Simplify Quantity A:
Quantity A: \( \frac{3x}{4}\)

Quantity B: \(3\)


From here we can multiply both quantities by 4 to get:
Quantity A: \( 3x\)

Quantity B: \(12\)


Divide both quantities by 3 to get:
Quantity A: \( x\)

Quantity B: \(4\)


Since it is given that \(4<x\), the correct answer is A



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