How Many Ways Can You Make Change for a Dollar Using Nickels, Dimes and Quarters?

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Using only nickels, dimes and quarters, there are 29 unique ways to make change for a dollar. It is helpful to use a systematic strategy for substituting coins in finding each unique combination totalling a dollar.

Because four quarters provide the simplest combination using the least coins, this is a helpful starting point. It is also helpful to use actual coins, as the problem is modeled so that a student working on this question can see the substitutions in action. Some students may find it helpful to make a chart to track solutions. This enables students to adapt learning in this scenario to bigger problems such as finding all ways to make change for a dollar using additional types of coins.