What is the maximum number of types of coins in the coin purse if the total value is $2.08, with equal amounts of each type?

To determine the maximum number of types of coins in the coin purse with a total value of $2.08, where there are equal amounts of each type, we first need to convert the total value into cents. $2.08 is equivalent to 208 cents.

Next, we need to consider how denominations of coins can be combined such that the total amounts to 208 cents. The common U.S. coin denominations are:

• 1 cent (penny)

• 5 cents (nickel)

• 10 cents (dime)

• 25 cents (quarter)

• 50 cents (half dollar)

• 100 cents (dollar)

To explore how many different types of coins can be used, we need to find distinct coin types that can each be included equally to reach the total of 208 cents. To maximize the number of types, the values should ideally be less than or equal to half of the total value to ensure that equal amounts can still allow reaching the total when combined.

For example, using coins with lower values allows for a greater variety without exceeding the total. Starting from 1 cent up to 2 cents, every combination of coins could be calculated based on how many coins of each type would sum