Question

If $x:y=3:5$, find the ratio $3x+4y:8x+5y$.

Answer 1

Compute the required ratio:

Given : $x:y=3:5$

Let $x=3k$ and $y=5k$

So we can write that

$$\begin{gathered} 3x+4y:8x+5y \\ =\frac{3\left(3k\right)+4\left(5k\right)}{8\left(3k\right)+5\left(5k\right)} \\ =\frac{\left(9k+20k\right)}{\left(24k+25k\right)} \\ =\left(\frac{29k}{49k}\right) \\ =\left(\frac{29}{49}\right) \end{gathered}$$

Hence the required ratio is $29:49$.