Question

You want to buy a candy bar from a vending machine that costs 55¢. The EXACT CHANGE light is on, and you have only a $1 bill. You ask the cashier to make change for your $1 bill so you will get 55¢ as part of the change. In how many ways can the cashier change your $1 bill so you will have the 55¢ you need to buy the candy bar?

a) 1
b) 2
c) 3
d) 4

Answer 1

There are four different ways the cashier can give change for a $1 bill that includes 55¢ for the vending machine purchase.

Step-by-step explanation:

You would like to buy a candy bar from a vending machine that costs 55¢, and you have a $1 bill but need to get exact change of 55¢. We're going to count the ways the cashier can give you change so that part of it will be exactly 55¢ for the candy bar. Since you have a $1 bill and need to make 55¢, the cashier needs to give you 45¢ in change, in addition to the 55¢. We need to look at how 45¢ can be made from coins.

Here are the possible coin combinations to make up 45¢, considering common US coins (quarters, dimes, nickels, and pennies):

• 1 quarter (25¢) + 2 dimes (10¢ + 10¢) = 45¢.
• 1 quarter (25¢) + 1 dime (10¢) + 1 nickel (5¢) + 5 pennies (1¢) = 45¢.
• 4 dimes (10¢ + 10¢ + 10¢ + 10¢) + 1 nickel (5¢) = 45¢.
• 3 dimes (10¢ + 10¢ + 10¢) + 3 nickels (5¢ + 5¢ + 5¢) = 45¢.

Therefore, there are four different ways for the cashier to give you 45¢, which when added to the 55¢ for the vending machine will use up the entire $1 bill.