Question 500675
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So far, you have it exactly right.


The next step is to add all of the values.  The value of the 10 cent stamps is, as you said, *[tex \Large .10n], the value of the 5 cent stamps is *[tex \Large .05(n\ +\ 2)] and the value of the 15 cent stamps is *[tex \Large .15(0.5n\ +\ 5)]


These three values add up to the total value of the stamps, namely $6.70.


Now, since I hate decimal fraction coefficients, I'm going to change everything from dollars and fractions of dollars to whole number of cents.  First,, $6.70 is nothing more than 670 cents, and the three values of the individual denominations become *[tex \Large 10n], *[tex \Large 5(n\ +\ 2)], and *[tex \Large 15\left(\frac{1}{2}n\ +\ 5\right)].  Now add it all up:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10n\ +\ 5(n\ +\ 2)\ +\ 15\left(\frac{1}{2}n\ +\ 5\right)\ =\ 670]


First let's get rid of the parentheses:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10n\ +\ 5n\ +\ 10\ +\ \frac{15}{2}n\ +\ 75\ =\ 670]


And then get the RHS constants over into the LHS by adding the opposites:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10n\ +\ 5n\ +\ \frac{15}{2}n\ =\ 585]


But we still have that pesky fraction -- with a denominator of 2.  Multiply by 2:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 20n\ +\ 10n\ +\ 15n\ =\ 1170]


Collect the terms in the RHS:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 45n\ =\ 1170]


Can you get it from here, remembering that *[tex \Large n] represents the number of 10-cent stamps?


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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