The food mart grocery store has a candy machine where you put in a quarter and 7 candies come out the machine. The machine holds 50 pounds of candy. Each pound of candy contains about 180 individual candies. How many total pieces of candy does the machine hold?

2700 candies
c(0) = 2700; c(n) = c(n-1) -7
c(n) = 2700 -7n
2693, 2686, 2679
Step-by-step explanation:
1. The number of candies in the machine is the product of the number of pounds of candy and the number of candies in a pound:
(15 lbs)(180 candies/lb) = 2700 candies
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2. c(0) = 2700; c(n) = c(n-1) -7 . . . . the new number of candies is 7 fewer than after the previous customer. After no customers, the number is the original 2700 candies.
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3. As the recursive formula tells us, the initial number of candies is 2700, and the number decreases at the rate of 7 per customer. The number remaining after n customers is ...
c(n) = 2700 -7n
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4. Evaluating the above formula for n=1, 2, 3, we get ...
c(1) = 2700 -7 = 2693 . . . . candies remaining after 1 customer
c(2) = 2700 -7·2 = 2686 . . . 2 customers
c(3) = 2700 -7·3 = 2679 . . . 3 customers

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