SOLUTION: Tickets in the ocean park cost 500$ for adults and 400$ for children. The management collected a total amount of not more than 80 000$ from 120 adults and children. What are the po

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Question 1172818: Tickets in the ocean park cost 500$ for adults and 400$ for children. The management collected a total amount of not more than 80 000$ from 120 adults and children. What are the possible number of adults and children in the Ocean Park? (find the inequality then GRAPH)
Found 2 solutions by mahikab, ikleyn:
Answer by mahikab(11)   (Show Source): You can put this solution on YOUR website!
Assume number of adults = a and number of children = c
Therefore,
a + c = 120 -------- (1)
and 500a + 400c <= 80000 -----(2)

When c=0, a <= 80000/500 = 160
When a=0, c <= 80000/400 = 200

So, the possible number of adults and children are:
All values of (a, c) satisfying inequation (2) where a <= 160, c <= 200
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

This problem is a SPECIAL CASE: one equation is combined with one inequality.


The equation is

    x + y = 120.    (x for adults, y for children)


The inequality is

    500x + 400y <= 80000


Simplify this inequality by dividing both sides by 100

    5x + 4y <= 800.


So, you have, actually, this system (one equation and one inequality)

     x +  y  = 120

    5x + 4y <= 800


Also, the problem assumes that both quantities x and y are NON-NEGATIVE

    x >= 0,  y >= 0.


On the plot, it looks like this


    


     Plot y = 120-x (red line) and y =   (green line)



The inequality represents all the points inside the triangle in QI under the green line.


The equation represents the red line.


So, the range for x is  0 <= x <= 120.

    The range for y is the same 0 <= y <= 120.


But x and y are not independent variables: they are interconnected by the equation x + y = 120.


This plot allows you to see the problem in whole and its solution, in particular.


The solution set is { the INTEGER points of the red line in QI }.


            It is the full analysis,  presented in the form  AS  IT  SHOULD  BE  DONE.



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