Final answer:
Harper pays $87 for a case of 48 glasses with a 40% trade-discount rate using the complement method.
Step-by-step explanation:
To find out how much Harper pays for a case of 48 glasses, we need to calculate the trade-discount rate. The complement method involves subtracting the discount rate from 100% and then multiplying it by the retail price. In this case, the trade-discount rate is 40%, so the complement is 60%. Therefore, Harper pays 60% of the retail price.
The retail price of a case of 48 glasses is $145. To calculate how much Harper pays, we multiply $145 by 60%, which is equal to 0.6. Hence, Harper pays $145 * 0.6 = $87.
Therefore, the correct answer is option a) $87.