Question

If x : y = 6 : 11, find (8x − 3y) : (3x + 2y).

Answer 1

$$\begin{gathered} \frac{x}{y}=\frac{6}{11} \\ \Rightarrow x=\frac{6y}{11} \end{gathered}$$

Now, we have:

$$\begin{gathered} \frac{8x-3y}{3x+2y} \\ =\frac{8\times {\displaystyle \frac{6y}{11}}-3y}{3\times {\displaystyle \frac{6y}{11}}+2y} \\ =\frac{48y-33y}{18y+22y} \\ =\frac{15y}{40y}=\frac{3}{8} \end{gathered}$$

∴ (8x − 3y) : (3x + 2y) = 3 : 8