Question

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

Answer 1

Let $$a = 8k$$ and $$b = 5k$$.

Substitute these values into the given expression:

$$\frac{7a + 5b}{8a - 9b} = \frac{7(8k) + 5(5k)}{8(8k) - 9(5k)}$$

Simplify the numerator and denominator:

$$\frac{56k + 25k}{64k - 45k} = \frac{81k}{19k} = \frac{81}{19}$$

Therefore, $$(7a + 5b) : (8a - 9b) = 81 : 19$$.