I'll just work the problem for you. You'll have to write it up using complete sentences and proper grammar, and filling in your own explanations. Let p = the number of pennies Let n = the number of nickels Let d = the number of dimes We have the equation:or multiplying through by 100, Since half the coins are nickels, we have We have the system: Substituting for in the first equation Divide through by 3: Since the left side is even, the right side must be even also, and positive. Therefore must be even and positive, too, Therefore d must be odd and no more than 11. Therefore there are 6 possibilities: d = 1, 3, 5, 7, 9, or 11 If , then becomes Substituting and into So one possibility is , , ------- If , then becomes Substituting and into So another possibility is , , ----------------- If , then becomes Substituting and into So another possibility is , , ------------- If , then becomes Substituting and into So another possibility is , , ------------- If , then becomes Substituting and into So another possibility is , , ------------- If , then becomes Substituting and into So another possibility is , , ------------- So all the 6 possibilities are 0 pennies, 11 nickels, 11 dimes, 22 coins, half of which are 11 nickels. 5 pennies, 14 nickels, 9 dimes, 28 coins, half of which are 14 nickels. 10 pennies, 17 nickels, 7 dimes, 34 coins, half of which are 17 nickels. 15 pennies, 20 nickels, 5 dimes, 40 coins, half of which are 20 nickels. 20 pennies, 23 nickels, 3 dimes, 46 coins, half of which are 23 nickels. 25 pennies, 26 nickels, 1 dimes, 52 coins, half of which are 26 nickels. Edwin