Had all received popcorn, the bill would have been 40×$1.75 = $70. The bill was $13.50 more than that. Each hot dog purchased in place of popcorn adds $0.50 to the bill, so the number of hot dogs must be ...
$13.50/$0.50 = 27
Of course, the remainder of the 40 items were popcorn, so 13 bags of popcorn.
27 hot dogs and 13 bags of popcorn were purchased.
