#### Answer

The number of nickels is 17.
The number of dimes is 33.
The number of quarters is 53.

#### Work Step by Step

Let n represent the number of nickels.
The number of dimes is 1 less than twice the number of nickels.
Twice the number of nickels means 2 $\times$ n = 2n.
1 less than twice the number of nickels means 2n - 1
So, the number of dimes is 2n - 1.
The number of quarters is 2 more than three times the number of nickels.
Three times the number of nickels means 3n.
2 more than three times the number of nickels means 3n + 2.
So, the number of quarters is 3n + 2.
The total number of coins is 103. We set up the following equation:
n + 2n - 1 + 3n + 2 = 103
6n + 1 = 103
6n = 102
Divide both sides by 6.
n = 17
The number of nickels is 17.
The number of dimes is 2 $\times$ 17 - 1 = 33.
The number of quarters is 3 $\times$ 17 + 2 = 53.