Final answer:
A machine holds 15 pounds of candy, with 180 candies per pound, totaling 2700 candies. The number of candies after a given number of customers is 2700 - 7 times the number of customers. The money in the machine is 0.25 dollars times the number of customers, and the machine will be empty after approximately 385 customers.
Step-by-step explanation:
Representing Candies and Money in the Machine
Let's first calculate the total number of candies in the machine. Given that there are 15 pounds of candy and each pound contains about 180 individual candies, we can multiply these two numbers to find the total amount of candy in the machine.
Total candies = 15 pounds × 180 candies/pound = 2700 candies
A. To represent the number of candies left in the machine after a given number of customers, we can set up a linear equation. As each child gets 7 candies per quarter, the number of candies decreases by 7 for each customer.
Candies left = Total candies - (7 candies × Number of customers)
B. To find out the total amount of money in the machine, we multiply the number of customers by the cost per play, which is one quarter (25 cents).
Money in machine = 0.25 dollars × Number of customers
Now, to find the number of customers before the machine is empty, we can take the total number of candies and divide by the number of candies given per quarter.
Number of customers before empty = Total candies / 7
This calculation results in 2700 candies ÷ 7 candies/customer ≈ 385.71, which we round down to 385 customers because you can't have a fraction of a customer.