Alvin has many apples. He gives 1/3 of his apples plus 2/3 of an apple to Bob.
He then gives 1/4 of his remaining apples plus half an apple to Chris.
Afterwards, he gives half of his remaining apples to David.
Lastly, he gives half of his remaining apples plus half an apple to Ed.
In the end, Alvin has 5 apples left. How many apples does Alvin have initially?
+14913 How many apples does Alvin have initially?
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x apples does Alvin have initially.
\(B= (\frac{1}{3}x+\frac{2}{3})\)
\(C=(\frac{1}{4}(x- (\frac{1}{3}x+\frac{2}{3}))+\frac{1}{2})\\ C= (\frac{1}{4}(x- \frac{1}{3}x-\frac{2}{3})+\frac{1}{2})\\ C=(\frac{1}{4}x- \frac{1}{12}x-\frac{1}{6}+\frac{1}{2})\\ \color{blue}C= (\frac{1}{6}x+\frac{1}{3})\)
\(D=(\frac{1}{2}(x- (\frac{1}{3}x+\frac{2}{3})-(\frac{1}{6}x+\frac{1}{3}))) \\ D=(\frac{1}{2}x- \frac{1}{6}x-\frac{1}{3}-\frac{1}{12}x-\frac{1}{6}) \\ \color{blue}D= (\frac{1}{4}x-\frac{1}{2})\)
\(E= (\frac{1}{2}(x-(\frac{1}{3}x+\frac{2}{3}) -(\frac{1}{6}x+\frac{1}{3})-(\frac{1}{4}x-\frac{1}{2}))+\frac{1}{2}) \\ E= (\frac{1}{2}x-\frac{1}{6}x-\frac{1}{3} -\frac{1}{12}x-\frac{1}{6}-\frac{1}{8}x+\frac{1}{4}+\frac{1}{2}) \\ \color{blue}E= (\frac{1}{8x}+\frac{1}{4})\)
\(x=(B)+(C)+(D)+(E)+5\)
\(x=((\frac{1}{3}x+\frac{2}{3})+(\frac{1}{6}x+\frac{1}{3}) + (\frac{1}{4}x-\frac{1}{2})+(\frac{1}{8}x+\frac{1}{4})+5)\\ x=0.875x+5.75\\ \frac{1}{8}x=5.75\)
\(x=46\)
46 apples does Alvin have initially.
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