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
click here to see the graph
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.