Final answer:
The amount of money collected in the candy machine for any number of customers is equal to the number of customers, as each quarter (per customer) dispenses 7 candies. With 15 pounds of candy and 180 candies per pound, there are 2700 candies in total. Therefore, the machine would appear empty and be ready for money collection after serving approximately 386 customers.
Step-by-step explanation:
The Food Mart candy machine holds 15 pounds of candy, and each pound contains about 180 individual candies. To represent the amount of money in the machine, we need to establish the relationship between the number of customers and the money collected. As every quarter inserted produces 7 candies, the total number of candies given out to n customers is 7n, where n is the number of customers. Since there are 180 candies in a pound, and the machine holds 15 pounds, there are a total of 15 × 180 = 2700 candies in the machine when it's full.
To find out how much money is in the machine for any given number of customers, we divide the total number of candies given to customers by the number of candies per quarter, which is 7. Therefore, the money collected for any number of customers, n, is (7n) / 7, which simplifies to n quarters or n / 4 dollars.
Assuming the machine is full at the start, the machine should look about empty when there are no candies left, which happens when all 15 pounds of candy have been dispensed. Since each customer takes 7 candies, and we have 2700 candies in total, the machine should look empty after 2700 / 7 ≈ 385.71 customers. However, the exact point at which the store owners should take the money out would depend on visual inspection or a predefined schedule.