The 24 Coins 3) There are 24 coins that total $2.90 -- nickels, dimes, and quarters. There are 4 more dimes than quarters. How many of each of these coins is there? 25x + 10(x + 4) + 5(20 -2x) = 290 25x + 10x +40 + 100 -10x = 290 25x + 140 = 290 25x = 150 x = 6 Since "x" is 6, then there are 6 quarters, (6 + 4) dimes, and (20-12) nickels. 1.50 (6 quarters) 1.00 (10 dimes) 0.40 (8 nickels) ------------------------- 2.90 (24 coins) As you can see in the formula above, the term for the dime takes the number value of "x" and adds 4 to it (since there are 4 more dimes than nickels). The term for the nickel includes "20-2x." Though there are 24 coins, we subtract the 4 that are being "reserved" for the dimes, to come up with this number in the formula. The "-2x" will then deduct the amount of the quarters and dimes from the nickels.