Question 343625
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Let *[tex \Large x] represent the number of 10 cent stamps.  Then the value of the 10 cent stamps is *[tex \Large 10x] cents.  Let *[tex \Large y] represent the number of 25 cent stamps.  Then the value of the 25 cent stamps is *[tex \Large 25y] cents.  For the sake of avoiding decimal fraction coefficients, let $14.00 be represented by 1400 cents.


There are 92 stamps, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ =\ 92]


Which can also be written:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 92\ -\ y]


The value of all the stamps is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10x\ +\ 25y\ =\ 1400]


But we can substitute from the earlier relationship:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10(92\ -\ y)\ +\ 25y\ =\ 1400]


Solve for *[tex \Large y] to get the number of quarters.  The number of dimes follows directly.


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