Problema Solution
An amateur theater group is converting a classroom to an auditorium for a forthcoming play. The group sells $3, $5, and $6 tickets, and receives exactly $503 from the sale of tickets. If the number of $5 tickets is twice the number of $6 tickets, and the number of $3 tickets is 1 more than 3 times the number of $6 tickets, how many tickets of each type are there?
Answer provided by our tutors
let
x = the number of $3 tickets
y = the number of $5 tickets
z = the number of $6 tickets
the group sells $3, $5, and $6 tickets, and receives exactly $503 from the sale of tickets
3x + 5y + 6z = 503
the number of $5 tickets is twice the number of $6 tickets
y = 2z
the number of $3 tickets is 1 more than 3 times the number of $6 tickets
x = 1 + 3z
by solving the system of equations
3x + 5y + 6z = 503
y = 2z
x = 1 + 3z
we find
x = 61 tickets
y = 40 tickets
z = 20 tickets
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