What is Bill’s average cost in cents for a bottle of soda, in terms of m and n?

He buys m bottles of brand A at $0.50
$0.50 = 0.5 * 100 = 50 cents
Total amount spent on m bottles of brand A = 50m
He buys m bottles of brand B at $0.60
$0.60 = 0.6 * 100 = 60 cents
Total amount spent on n bottles of B = 60n
$$Average\ \cos t=\frac{Total\ \cos t\ of\ all\ bottles\ of\ soda}{No.\ of\ bottles\ of\ soda}$$ .$$=\frac{50m+60n}{m+n}$$

This validates option D as our choice of answer.