Final answer:
The cashier’s algorithm is used to make change with the least number of coins possible, starting with the largest coin denominations. For 87 cents, the correct change is 3 quarters, 1 dime, and 2 pennies. For 99 cents, it's 3 quarters, 2 dimes, and 4 pennies. For 60 cents, it's 2 quarters and 1 dime. Option C is correct.
Step-by-step explanation:
The cashier’s algorithm provides an efficient way to make change for a given amount using the least number of coins possible. The goal is to use the largest coin denominations first and then proceed to smaller denominations as needed. Here's how you would use the algorithm for the following amounts:
87 cents: First, determine how many quarters can fit into 87 cents. Since a quarter is worth 25 cents, you can fit 3 quarters into 87 cents which gives you 75 cents. Subtract this from 87 cents to get 12 cents remaining. Next, use a dime (10 cents) to get to 85 cents, leaving 2 cents, which can be made with two pennies. Therefore, for 87 cents, the correct change would be 3 quarters, 1 dime, 0 nickels, and 2 pennies.
99 cents: Using quarters first, you can fit 3 quarters into 99 cents to make 75 cents. Subtract this from 99 cents to get 24 cents remaining. Use two dimes (20 cents) to get to 95 cents, leaving 4 cents, which can be made with four pennies. Therefore, the correct change for 99 cents would be 3 quarters, 2 dimes, 0 nickels, and 4 pennies.
60 cents: You can use 2 quarters to make 50 cents, leaving 10 cents, which can be made with one dime. No nickels or pennies are needed. Therefore, the correct change for 60 cents is 2 quarters, 1 dime, 0 nickels, and 0 pennies.
Remembering that 1 dollar equals 100 pennies helps understand that we need more of a smaller unit to equal a larger unit, similar to other units of length, weight, and capacity. The given examples demonstrate how we convert between coin values to make an exact amount in cents.