Question 188201
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Lori has <i>x</i> eggs, and if she gives away 5, she will have <i>x</i> - 5 eggs.


Cameron has <i>y</i> eggs, and if he gets 5 from Lori, he will have <i>y</i> + 5 eggs.


Three times as many as Lori has after she gives away 5 is 3(<i>x</i> - 5) = 3<i>x</i> - 15 and this is the same as what Cameron has after he gets 5, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  3x - 15 = y + 5]


By a similar analysis, if Cameron gives Lori 5 eggs, we have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  x + 5 = y - 5]


Solve this second equation for <i>y</i> by adding 5 to both sides:


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


Substitute this expression for <i>y</i> into the other equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  3x - 15 = (x + 10) + 5]


And solve for <i>x</i>:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  3x - 15 = x + 15]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  2x = 30]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  x = 15]


So Lori starts out with 15 eggs.


Substitute <i>x</i> = 15 into either of the equations:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  y = (15) + 10 = 25]


So Cameron starts out with 25 eggs.


15 minus 5 = 10, and 25 plus 5 = 30, and 30 is 3 times 10.


15 plus 5 is 20 and 25 minus 5 is 20.  Answer checks.



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