Question

If x : y = 8 : 9, find the ratio (7x − 4y) : 3x + 2y.

Answer 1

It is given that
x : y = 8 : 9 ⇒ $\frac{x}{y}$ = $\frac{8}{9}$
Now, 7x $-$ 4y : 3x + 2y
= $\frac{7x-4y}{3x+2y}$
= $\frac{{\displaystyle \frac{7x-4y}{y}}}{{\displaystyle \frac{3x+2y}{y}}}$ {dividing the numerator and the denominator by 'y'}
= $\frac{7\left({\displaystyle \frac{x}{y}}\right)-4}{3\left({\displaystyle \frac{x}{y}}\right)+2}$ = $\frac{7\left({\displaystyle \frac{8}{9}}\right)-4}{3\left({\displaystyle \frac{8}{9}}\right)+2}$ = $\frac{{\displaystyle \frac{56}{9}}-4}{{\displaystyle \frac{24}{9}}+2}$
= $\frac{{\displaystyle \frac{56-36}{9}}}{{\displaystyle \frac{24+18}{9}}}$ = $\frac{20}{42}$ = $\frac{10}{21}$
Hence, 7x $-$ 4y : 3x + 2y = 10 : 21.