Decoding Ratios: Solve the Equation for 2x : (7y : 4x)

To solve this problem, we'll simplify the expression $2x : (7y : 4x)$ using properties of division:

• Step 1: Recognize $a : (b : c) = a \times \frac{c}{b}$. This changes the nested division into a singular operation.
• Step 2: Substitute into our expression: $2x : (7y : 4x) = 2x \times \frac{4x}{7y}$.
• Step 3: Simplify the expression $= 2 \times \frac{4x^2}{7y}$.
• Step 4: Calculate the product: $= \frac{8x^2}{7y}$.
• Step 5: Convert to a mixed number if necessary: $= 1\frac{1}{7}\frac{x^2}{y}$.

Therefore, the solution to the problem is $\frac{8x^2}{7y}$, which can be expressed as a mixed number $1\frac{1}{7}\frac{x^2}{y}$.