Question 1121102
<font face="Times New Roman" size="+2">


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x\ +\ 10y\ =\ 60]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x,\,y\ \geq\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x\ =\ -10y\ +\ 60]


Clearly *[tex \Large y\ <\ 6] otherwise *[tex \Large x\ <\ 1]


So *[tex \Large y] is bounded above and below by *[tex \LARGE 1\ \leq\ y\ \leq\ 5] and restricted to the integers (no fractional boxes of 10 tomatoes).


In other words:  *[tex \Large y\ \in\ \{1,\,2,\,3,\,4,\,5\}]


Test these values in *[tex \Large 4x\ =\ -10y\ +\ 60] to eliminate values of  *[tex \Large y] that do not result in integer values of  *[tex \Large x]
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
{{n}\choose{r}}
</font>