Question 189863
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Let <i>d</i> be the number of dimes and let <i>q</i> be the number of quarters.  Then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  d + q = 82]


The total amount of money is $13.  It will be convenient to represent this as 1300 cents.  Since there are <i>d</i> dimes and each of them is worth 10 cents, the total value of all of the dimes is 10<i>d</i> cents.  Likewise the total value of all of the quarters is 25<i>q</i> cents.  Since there were only dimes and quarters in the change jar, the value of the dimes plus the value of the quarters must equal the total amount of money in the jar, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  10d + 25q = 1300]


But since

*[tex \LARGE \ \ \ \ \ \ \ \ \ \  d + q = 82]


We can also say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  q = 82 - d]


Having an expression for the quantity <i>q</i> in terms of <i>d</i> allows us to make the following substitution:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  10d + 25(82 - d) = 1300]


Solve the equation for <i>d</i> to determine the number of dimes, then subtract the number of dimes from 82 to determine the number of quarters.



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