Question 368860
<font face="Garamond" size="+2">


Let *[tex \Large x] represent the number of $20/set sets and *[tex \Large y] represent the number of $45/set sets.  Then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ =\ 250]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 20x\ +\ 45y\ =\ 6800]


Elimination is the easiest for this system.


Multiply the first equation by *[tex \Large -20]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -20x\ -\ 20y\ =\ -5000]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 20x\ +\ 45y\ =\ 6800]


Add the two equations:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -20x\ +\ 20x\ -\ 20y\ +\ 20y\ =\ -5000\ +\ 6800]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 25y\ =\ 1800\ \Leftrightarrow\ y\ =\ 72]


From which you get:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 72\ =\ 250]


hence


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 178]


Check by substituting the calculated values back into the two equations to ensure that both equations are true statements when the values are inserted.


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>