Question 182833
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The amount of change was *[tex \Large 20.00 - 9.25 = 11.75].  Easier to use whole numbers so change that to 1175 cents.


Let <i>q</i> be the number of quarters and <i>f</i> be the number of half-dollars.  Since there were 30 coins:


*[tex \LARGE \text{          }\math q + f = 30 \ \ \Rightarrow\ \ f = 30 - q]


The value of the quarters is 25 cents times the number of quarters, or *[tex \Large 25q].  Likewise, the value of the half-dollars is *[tex \Large 50f].


The value of the quarters plus the value of the half-dollars must total the amount of change, or 1175 cents.


*[tex \LARGE \text{          }\math 25q + 50f = 1175]


Substitute from the earlier relationship:


*[tex \LARGE \text{          }\math 25q + 50(30 - q) = 1175]  


Solve for <i>q</i> to get the number of quarters, subtract from 30 to get the number of half-dollars.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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