Question

Jennifer's school is selling tickets to a chorus concert. On the first day of ticket

sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38.
On the second day of ticket sales, the school sold another 3 senior citizen tickets
and 2 child tickets for $52.

Answer 1

• senior: $8
• child: $14

Explanation:

The given price relations allow us to write two equations involving the prices of the tickets. Those can be solved to find ticket prices.

Let s and c represent the prices of senior and child tickets respectively. Then the described sales can be written as ...

3s +c = 38 . . . . first day's sales

3s +2c = 52 . . . second day's sales

__

Subtracting the first equation from the second eliminates the s variable and gives the price of a child ticket:

(3s +2c) -(3s +c) = (52) -(38)

c = 14 . . . . . simplify

Then the price of a senior citizen ticket can be found using the first equation:

3s +14 = 38 . . . . . substitute for c

3s = 24 . . . . . . . subtract 14

s = 8 . . . . . . . divide by 3

The price of a senior citizen ticket is $8; the price of a child ticket is $14.