Question

El) CC.11 Solve a system of equations using elimination: word problems 297

Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
The box office at a theater is selling tickets for a series of rock concerts. So far, they have
sold 79 balcony tickets and 27 general admission floor tickets for Friday's show, for a total of
$5,550 in receipts. For Saturday's show, 79 balcony tickets and 36 general admission floor
tickets have been sold, equaling $5,820 in receipts. How much does each ticket cost?
A balcony seat ticket costs $
, and a general admission floor ticket costs $
Submit
Work it out
Video

Answer 1

• balcony: $60
• general admission: $30

Explanation:

Given that 79 balcony and 27 general admission tickets sell for $5550, and 79 balcony and 36 general admission tickets sell for $5820, you want the cost of each kind of ticket.

Equations

The equations representing the sales are ...

79b +27g = 5550

79b +36g = 5820

Solution

Subtracting the first equation from the second, we have ...

(79b +36g) -(79b +27g) = (5820) -(5550)

9g = 270 . . . . . . . . . simplify

g = 30 . . . . . . . divide by 9

79b +27(30) = 5550 . . . . . . substitute into the first equation

79b = 4740 . . . . . . . . . . subtract 810 & simplify

b = 60 . . . . . . . divide by 79

A balcony seat ticket costs $60; a general admission floor ticket costs $30.