Inequality solution verification(positive solution) I have the following system of equation where a

Ryan Reynolds 2022-05-21 Answered
Inequality solution verification(positive solution)
I have the following system of equation where all the free variables live in the integers that is are allowed to be integers only.
x = l
y = 5 n 2 l + 25
z = 10 2 n
For l , n N
I need to compute how many positive solutions are there so I computed the following inequalities:
x > 0 l > 0
y > 0 n > 5 + 2 l / 5
z > 0 n < 5
To get how many solution we keep a fixed l and see how many n we get and do that for each n until we get values that pop us out of the inequality for example for l = 1 we have n > 4.6 hence we have 4 n < 5 so in this case their is 10 solutions and we proceed like this I just want to verify my answer I got 105 possible positive solutions is that correct?
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Answers (1)

antantil0
Answered 2022-05-22 Author has 9 answers
Mathematically Your equations are equivalent to :
5 ( n + 5 ) > 2 l > 0 5 > n
so for fixed l we have 2 l 5 < n + 5 < 10 this means that 0 < l 24 and the number of solution possible value of n with l fixed is exactly is 9 2 l 5 and so the number of solution is:
using calculator: we compute the sum, and we get the total number 216 110 = 106
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