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(834)   (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
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