Question 642048
<font face="Times New Roman" size="+2">
If you have a total of *[tex \LARGE T] objects of 2 types, let the number of each be referred to as *[tex \LARGE x_1] and *[tex \LARGE x_2].  Then, if the total value of all of the objects is *[tex \LARGE V] when the value of each object type 1 is *[tex \LARGE v_1] and the value of each object type 2 is *[tex \LARGE v_2], you can write the following two equations:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ +\ x_2\ =\ T]


and 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ v_1x_1\ +\ v_2x_2\ =\ V]


Solve for *[tex \LARGE x_1] by elimination:


Multiply the first equation by *[tex \LARGE -v_2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -v_2x_1\ -\ v_2x_2\ =\ -v_2T]


Then add the two equations:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (v_1\,-\,v_2)x_1\ +\ 0x_2\ =\ V\ -\ v_2T]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ =\ \frac{V\ -\ v_2T}{v_1\,-\,v_2}]


Once you know *[tex \LARGE x_1], you can substitute into equation 1 to get a single variable equation in *[tex \LARGE x_2] that can be solved by ordinary means.


Note: in your specific problem be careful of your monetary units.  The per each values of the stamps are given in cents, whereas the total value is given in dollars.  My recommendation for this problem, so as to avoid decimal fraction coefficients, would be to convert $1.50 to 150 cents.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>