Question

1.

destions. Show your wor
For a recent Broadway musical, orchestra main floor seats cost $148 each, and
balcony seats cost $65 each. A theatre group purchased 30 tickets for an upcoming
show in June. If the total cost of the 30 tickets was $2,614, how many of each type
of ticket did the theatre group buy?
Number of orchestra tickets
Number of balcony tickets

Answer 1

Number of orchestra tickets = 8

Number of balcony tickets = 22

Explanation:

Let the number of orchestra tickets be x and number of balcony tickets be y.

So, cost of x orchestra tickets = $148 × x = $148x

Cost of y balcony tickets = $65 × x = $65y

Also given, total number of tickets = 30

Cost of 30 tickets = $2,614

So, the system of equations that can ne formed is :

x + y = 30 ....eq 1

148x + 65y = 2614 ....eq 2

Multiplying eq 1 by 148 and subtracting eq 2 by it,

148x + 148y - 148x - 65y = 4440 - 2614

83y = 1826

y = 1826/83 = 22

Substituting y = 22 in eq 1,

x + 22 = 30

So, x = 30 - 22 = 8

Thus,

Number of orchestra tickets = 8

Number of balcony tickets = 22