Elementary Algebra

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.