Question 326894
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Let *[tex \Large d] represent the number of dimes.

Let *[tex \Large q] represent the number of quarters.

Since dimes are worth 10 cents, the value of all of the dimes in cents is *[tex \Large 10d]

Likewise the value of all of the quarters is *[tex \Large 25q]

Since I expressed the value of the coins in terms of cents, let's express the total value of the coins in cents as well.  *[tex \Large \$7.00 = 700] cents.

We know there are 46 coins, so:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ +\ q\ =\ 46]

And we know the total value of the coins is 700 cents, so:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10d\ +\ 25q\ =\ 700]

Rearrange the first equation:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 46\ -\ q]

Substitute:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10(46\ -\ q)\ +\ 25q\ =\ 700]

Now all you need to do is solve for *[tex \Large q] and *[tex \Large d] follows directly.

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