If a coin purse contains equal amounts of pennies, nickels, and dimes summing to $2.08, how many of each type of coin are present?

To find the number of each type of coin in the purse, we set up the problem based on the information given. Let's denote the number of pennies, nickels, and dimes as ( x ). Since there are equal amounts of each coin, we can express the total value contributed by each type of coin as follows:

• Pennies are worth $0.01 each, so the total from pennies is ( 0.01x ).

• Nickels are worth $0.05 each, so the total from nickels is ( 0.05x ).

• Dimes are worth $0.10 each, so the total from dimes is ( 0.10x ).

The total value of all coins is given as $2.08. Therefore, we can write the equation for the total value of the coins:

[

0.01x + 0.05x + 0.10x = 2.08

]

Combining the terms on the left side gives us:

[

(0.01 + 0.05 + 0.10)x = 2.08

]

[

0.16x = 2.08

]

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