If a : b = 8 : 5, find (7a + 5b) : (8a − 9b).

Given,

a : b = 8 : 5

Let a = 8x and b = 5x.

Substituting values in $\dfrac{7a + 5b}{8a − 9b}$ we get,

$\Rightarrow \dfrac{7(8x) + 5(5x)}{8(8x) - 9(5x)} \\[1em] \Rightarrow \dfrac{56x + 25x}{64x - 45x} \\[1em] \Rightarrow \dfrac{81x}{19x} \\[1em] \Rightarrow \dfrac{81}{19}.$

Hence, 7a + 5b : 8a − 9b = 81 : 19.