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No calc please

 Jun 8, 2019

Best Answer 

 #1
avatar+8853 
+3

Let's say it starts wih  x  fish.

 

number of fish left after John leaves _ \(=\ \frac23({\color{Aquamarine}x}-1)\ =\ \frac23x-\frac23\)
number of fish left after Joe leaves

 

 

 

\(=\ \frac23(\ {\color{Aquamarine}\frac23x-\frac23}\ -1)\ =\ \frac49x-\frac{10}{9}\)
number of fish left after _James_ leaves

 

\(=\ \frac23(\ {\color{Aquamarine}\frac49x-\frac{10}{9}}\ -1)\ =\ \frac{8}{27}x-\frac{38}{27}\)

 

The smallest positive integer value of  x  that makes  \(\frac{8}{27}x-\frac{38}{27}\)  a positive integer is  25 .

 

By looking at a graph we can check this:  https://www.desmos.com/calculator/mivvh3t6in

 

So the minimum possible number of fish before John threw out the first fish is  25 .

 Jun 8, 2019
 #1
avatar+8853 
+3
Best Answer

Let's say it starts wih  x  fish.

 

number of fish left after John leaves _ \(=\ \frac23({\color{Aquamarine}x}-1)\ =\ \frac23x-\frac23\)
number of fish left after Joe leaves

 

 

 

\(=\ \frac23(\ {\color{Aquamarine}\frac23x-\frac23}\ -1)\ =\ \frac49x-\frac{10}{9}\)
number of fish left after _James_ leaves

 

\(=\ \frac23(\ {\color{Aquamarine}\frac49x-\frac{10}{9}}\ -1)\ =\ \frac{8}{27}x-\frac{38}{27}\)

 

The smallest positive integer value of  x  that makes  \(\frac{8}{27}x-\frac{38}{27}\)  a positive integer is  25 .

 

By looking at a graph we can check this:  https://www.desmos.com/calculator/mivvh3t6in

 

So the minimum possible number of fish before John threw out the first fish is  25 .

hectictar Jun 8, 2019

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