# SOLUTION: A collection of 65 coins consisting of dimes, quarters, and half-dollars has a value of \$16.30. There are two times as many quarters as dimes. Find the number of each kind of coin.

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 Click here to see ALL problems on Word Problems With Coins Question 263943: A collection of 65 coins consisting of dimes, quarters, and half-dollars has a value of \$16.30. There are two times as many quarters as dimes. Find the number of each kind of coin. Answer by CharlesG2(828)   (Show Source): You can put this solution on YOUR website!A collection of 65 coins consisting of dimes, quarters, and half-dollars has a value of \$16.30. There are two times as many quarters as dimes. Find the number of each kind of coin. H half-dollar, Q quarter, D dime 2 times as many quarters as dimes H + Q + D = 65 (replace Q with 2*D) H + 2 * D + D = 65 H + 3 * D = 65 (solve for H for later) H = 65 - 3 * D 0.50 * H + 0.25 * Q + 0.10 * D = 16.30 (multiply both sides by 100) 50 * H + 25 * Q + 10 * D = 1630 (replace Q with 2*D) 50 * H + 25 * (2 * D) + 10 * D = 1630 50 * H + 50 * D + 10 * D = 1630 50 * H + 60 * D = 1630 (divide both sides by 10) 5 * H + 6 * D = 163 (plug in H = 65 - 3 * D) 5 * (65 - 3 * D) + 6 * D = 163 325 - 15 * D + 6 * D = 163 325 - 9 * D = 163 -9 * D = -162 9 * D = 162 D = 18 plug in D = 18 into H = 65 - 3 * D H = 65 - 3 * 18 H = 65 - 54 H = 11 so we got 18 dimes and since we had twice as many quarters as dimes that would be 36 quarters 65 coins - 18 coins - 36 coins = 47 coins - 36 coins = 11 coins check: 0.50 * 11 + 0.25 * 36 + 0.10 * 18 5.50 + 9.00 + 1.80 14.50 + 1.80 16.30 which is the amount we had and wanted