If a : b = 3 : 2, find ratio (4a + 5b) : (4a - 5b).

Question: If a : b = 3 : 2, find ratio (4a + 5b) : (4a - 5b).

Solution:
(4a + 5b) : (4a - 5b)
= b(4a/b + 5) : b (4a/b - 5)
= (4 × 3/2 + 5) : (4 × 3/2 - 5)
= (6 + 5) : (6 - 5)
= 11 : 1