Question 657439
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Sometimes appearances can be deceiving.  However, that is NOT the case here.  Your equation looks completely wrong for the most obvious of reasons; it is completely wrong.  That fact leads us to the very best starting place:  The beginning.


If there are 42 children and *[tex \LARGE \frac{2}{3}] of them are boys, then there are *[tex \LARGE \frac{2}{3}\,\cdot\,42\ =\ 28] boys; from which it should be obvious (since *[tex \LARGE \frac{1}{3}] is half of *[tex \LARGE \frac{2}{3}]) that there are 14 girls.


Let *[tex \LARGE x] represent the number of stickers each boy received, and then *[tex \LARGE 2x] must be the number of stickers each girl received.  Since there are 28 boys each of whom received *[tex \LARGE x] stickers, the total number of stickers received by boys is *[tex \LARGE 28x].  Similarly, the total number of stickers received by girls is *[tex \LARGE 14(2x)\ =\ 28x].  Then, since the sum of *[tex \LARGE \frac{1}{3}] and *[tex \LARGE \frac{2}{3}] is 1, we can be certain that there were no transgender people in the group of children (hey, you never know these days) so we can make the assertion that the number of stickers given to boys plus the number of stickers given to girls is equal to the total number of stickers given. So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 28x\ +\ 28x\ =\ 840]


Solve for *[tex \LARGE x] and then calculate *[tex \LARGE 2x]


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