If x: y = 1: 2, find the value of (2x + 3y) : (x + 4y).
 

Given; x : y = 1 : 2 means $\frac{\mathrm{x}}{\mathrm{y}} = \frac{1}{2}$

Now, (2x + 3y) : (x + 4y) =$\frac{ (2\mathrm{x} + 3\mathrm{y})}{(\mathrm{x} + 4\mathrm{y})}$

 Now, Divide the numerator and denominator by y, and we get: 

$\Rightarrow \frac{\left[{\displaystyle \frac{(2\mathrm{x} + 3\mathrm{y})}{\mathrm{y}}}\right] }{\left[\frac{(\mathrm{x} + 4\mathrm{y})}{2}\right]}=\frac{ \left[2\right({\displaystyle \frac{\mathrm{x}}{\mathrm{y}}}) + 3] }{\left[\right(\frac{\mathrm{x}}{\mathrm{y}}) + 4]}$

By putting $\frac{\mathrm{x}}{\mathrm{y}} = \frac{1}{2}$, we get:

 $\Rightarrow \frac{ \left[2\right({\displaystyle \frac{\mathrm{x}}{\mathrm{y}}}) + 3] }{\left[\right(\frac{\mathrm{x}}{\mathrm{y}}) + 4]} = \frac{ \left[2\right({\displaystyle \frac{1}{2}}) + 3] }{\left[\right(\frac{1}{2}) + 4]} = \frac{8}{9} = 8 : 9$

Therefore the value of (2x + 3y) : (x + 4y) = 8 : 9