Problema Solution

tickets in a play cost 250 pesos for adults and 200 pesos for children. the sponsor of the show collected a total amount of not more than 22,000 pesos from more than 100 adults and children watched the play.find the number who watched the play.

Answer provided by our tutors

let


a = the number of adults

c = the number of children


the sponsor of the show collected a total amount of not more than 22,000 pesos


250a + 200c <= 22000


more than 100 adults and children watched the play


a + c > 100


from the graph of the system of inequalities


250a + 200c <= 22000

a + c > 100


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we see that for


a = 40


c = 60


250*40 + 200*60 = 22000

a + c = 40 + 60 = 100


for c = 101


a <= (22000 - 200*101)/250

a <= 7.2


lets say a = 7 we have the following


a + c = 101 + 7 = 108 > 100


250*7 + 200*101 = 21,950 < = 22000


thus one solution is 101 children and 7 adults or total of 108 people that watched the play.