If a : b = 3 : 4 and b : c = 8 : 9, then (a + b) : (b + c) is:

Make b the same in both ratios: a : b = 6 : 8 and b : c = 8 : 9, so a : b : c = 6 : 8 : 9. Then (a + b) : (b + c) = 14 : 17. (Adding the given ratios term by term as (3 + 4) : (8 + 9) = 7 : 17 or (3 + 8) : (4 + 9) = 11 : 13 is meaningless until the two ratios are put on a common value of b.)