SOLUTION: A local concert sells out for their show. They sell all 500 tickets for a total purse of $8,070.00. The tickets were priced at $15 for students (s), $12 for children (c), and $18
Question 1138773: A local concert sells out for their show. They sell all 500 tickets for a total purse of $8,070.00. The tickets were priced at $15 for students (s), $12 for children (c), and $18 for adults (a). If the band sold three times as many adult tickets as children’s tickets, how many of each type was sold?
This problem can be a good example for comparing the method of solving the problem with three variables (as suggested by the statement of the problem) to the method of solving it with a single variable.
While it is important to know how to solve a problem involving a system of equations in several variables, very often the amount of effort required to solve the problem is far less with a single equation in one variable.
A solution using 3 variables....
c = number of children's tickets
s = number of student tickets
a = number of adult tickets
(1) the total number of tickets was 500
(2) the number of adult tickets was 3 times the number of children's tickets
(3) the total cost of the tickets was $8070
Substitute (2) in (1) and (3) to eliminate a, giving two equations in s and c:
(4) -->
(5) -->
Eliminate s between (4) and (5) by multiplying (4) by -15 and adding:
The number of children's tickets was c = 95.
Then the number of adult tickets was 3c = 285.
The total number of adult and children's tickets was 95+285 = 380; so the number of student tickets was 500-380 = 120.
let x = number of children's tickets
then 3x = number of adult tickets (3 times as many as children's)
and (500-4x) = number of student tickets (the total of 500, minus the adult and children's tickets)
