Question

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

Answer 1

It is given that
x : y = 3 : 5 ⇒ $\frac{x}{y}=\frac{3}{5}$
Now, 3x + 4y : 8x + 5y
= $\frac{3x+4y}{8x+5y}$
= $\frac{{\displaystyle \frac{3x+4y}{y}}}{{\displaystyle \frac{8x+5y}{y}}}$ {dividing the numerator and the denominator by 'y'}
= $\frac{3\left({\displaystyle \frac{x}{y}}\right)+4}{8\left({\displaystyle \frac{x}{y}}\right)+5}$ = $\frac{3\left({\displaystyle \frac{3}{5}}\right)+4}{8\left({\displaystyle \frac{3}{5}}\right)+5}$ = $\frac{{\displaystyle \frac{9}{5}}+4}{{\displaystyle \frac{24}{5}}+5}$
= $\frac{{\displaystyle \frac{9+20}{5}}}{{\displaystyle \frac{24+25}{5}}}$ = $\frac{{\displaystyle \frac{29}{5}}}{{\displaystyle \frac{49}{5}}}$ = $\frac{29}{49}$