Ok, let's settle this with a simultaneous equation...
0.25 X + 0.10 Y = 12.05
X + Y = 59
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This means that:
X = 59 - Y
Which means that:
0.25 (59 - Y) + 0.10 Y = 12.05
0.25 59 - 0.25 Y + 0.10 Y = 12.05
Y (0.10 - 0.25) = 12.05 - 0.25 59
-0.15 * Y = -2.7
Y = (-2.7)/(-0.15)
Y = 18
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X + Y = 59
Therefore:
X + 18 = 59
X = 59 - 18
X = 41
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There are 41 quarters and 18 dimes.