Question

The school that Trevon goes to selling tickets to the annual dance competition. On the first day of tickets sales the school sold 12 senior citizen tickets and 5 child tickets for a total of 85$. The school took in $75 on the second day by selling 6 senior citizen tickets and 9 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

Answer 1

Answer:

  both kinds of tickets are $5 each

Step-by-step explanation:

Let s and c represent the dollar costs of a senior ticket and child ticket, respectively. The problem statement describes two relationships:

  12s + 5c = 85 . . . . . revenue from the first day of sales

  6s + 9c = 75 . . . . . . revenue from the second day of sales

Double the second equation and subtract the first to eliminate the s variable.

  2(6s +9c) -(12s +5c) = 2(75) -(85)

  13c = 65 . . . . . simplify

  65/13 = c = 5 . . . . . divide by the coefficient of c

Substitute this value into either equation. Let's use the second one.

  6s + 9·5 = 75

  6s = 30 . . . . . . . subtract 45

  30/6 = s = 5 . . . divide by the coefficient of s

The price of a senior ticket is $5; the price of a child ticket is $5.