Problema Solution
tickets for a dance are sold for 5 dollars to seniors and 7 dollars to juniors. the dancehall can hold 560 students. how many of each type of ticket must be sold to raise at least $3500
Answer provided by our tutors
let
x = the number of $5 tickets
y = the number of $7 tickets
if we consider that one student buys only one ticket then we have
x + y <=560
the tickets sold must raise at least $3500
5x + 7y >=3500
by solving the system of inequalities
x + y <=560
5x + 7y >=3500
x >= 0
y >= 0
we find
y <= 560 - x
y >= 500 - 5x/7
x > = 0
y > = 0
if we graph these inequalities we see that at least 350 junior tickets and maximum 210 senior tickets must be sold.