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

Answer:

• senior: $8
• child: $14

Step-by-step 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

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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.