Question 273447
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No, I won't answer all.  I'll show you how to do one of them, and the others are done in the same manner.


Let *[tex \Large x] represent the number of 32 cent stamps and let *[tex \Large y] represent the number of 38 cent stamps.  The value of all of the 32 cent stamps is then *[tex \Large 32x] cents.  Likewise, the value of all of the 38 cent stamps is *[tex \Large 38y] cents.


Since we know there are 42 stamps we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ =\ 42]


And since we know the value of all of the stamps is $14.82, which is to say 1482 cents, we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 32x\ +\ 38y\ =\ 1482]


Solve the first equation for either of the variables:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 42\ -\ y]


And then substitute:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 32(42\,-\,y)\ +\ 38y\ =\ 1482]


Now all you have to do is solve for *[tex \Large y].  The value of *[tex \Large x] follows directly.


The other two problems are solved in the same way.  Create an equation that describes the numbers of things and then an equation that describes the value of things.


In the third problem, use *[tex \Large x] for the 50 cent valentines.  Then *[tex \Large 2x\ +\ 3] is the number of 25 cent valentines and *[tex \Large x\ -\ 1] is the number of 75 cent valentines.  Don't forget to change $5.25 to 525 cents. 



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