Say there is a cat that in three days eat 12 fishes.Say that each day the cat eats more than the day before.Say that the last day the cat has eaten less than the addition of the two previous days. { x + y + z = 12 z &gt; y &gt; x z &lt; x + y How am I supposed to solve this?

Question

Say there is a cat that in three days eat 12 fishes.Say that each day the cat eats more than the day before.Say that the last day the cat has eaten less than the addition of the two previous days.      {                            x          +          y          +          z          =          12                                      z          &amp;gt;          y          &amp;gt;          x                                      z          &amp;lt;          x          +          y                        How am I supposed to solve this?

Samantha Reid · Accepted Answer

To do a graphical solution, you can use the equality   z  =  12  −  x  −  y       in the inequalities to get   12  &amp;lt;  2  x  +  2  y  ,     y  &amp;gt;  x  ,     12  &amp;gt;  2  y  +  x  .      . You can plot these three as you are used to, shading the proper side of the lines. Then as you are looking for integer solutions you have to look for lattice points in the allowable region.

Dania Mueller · Accepted Answer

All variables must obviously be non-negative and less or equal 12. Combining the first equality and the last inequality we get   z  ≤  6.   z must also satisfy   z  ≥  4 because   z  &amp;lt;  4 would imply   y  &amp;lt;  4,   x  +  y  +  z  &amp;lt;  12. Similarly,   x must satisfy   x  ≤  4 because   x  &amp;gt;  4 would imply   y  &amp;gt;  4,   x  +  y  +  z  &amp;gt;  12.So, all solutions are obtained by choosing  x  ∈  [  0  ,  4  ]  z  ∈  [  4  ,  6  ]  y  =  12  −  (  x  +  z  )f only positive solutions are allowed, then   x  ∈  (  0  ,  4  ]

Say there is a cat that in three days eat 12 fishes. Say that each day the cat eats more than the d

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