Answer:
3 dimes, 5 nickels, and 9 pennies
Explanation:
Let's solve the problem step by step.
Let's assume the number of dimes as 'x'.
According to the given information, there are two more nickels than dimes. So, the number of nickels is 'x + 2'.
Also, there are three times as many pennies as dimes. Therefore, the number of pennies is '3x'.
Now, let's calculate the total value of the coins:
The value of each dime is 10 cents, so the value of 'x' dimes is 10x cents.
The value of each nickel is 5 cents, so the value of 'x + 2' nickels is 5(x + 2) cents.
The value of each penny is 1 cent, so the value of '3x' pennies is 1(3x) cents.
Adding up the values of each type of coin should give us the total value, which is 64 cents:
10x + 5(x + 2) + 1(3x) = 64
Now, let's solve the equation:
10x + 5x + 10 + 3x = 64
18x + 10 = 64
18x = 64 - 10
18x = 54
x = 54 / 18
x = 3
So, the number of dimes is 3. Now, let's find the number of nickels and pennies:
Number of nickels = x + 2 = 3 + 2 = 5
Number of pennies = 3x = 3 * 3 = 9
Therefore, there are 3 dimes, 5 nickels, and 9 pennies in the collection.