The school that Trevon goes to is selling tickets to the annual dance competition. On the first day of ticket sales, the school sold 12 senior citizen tickets and 5 child tickets for a total of [tex]$85[/tex]. On the second day, the school took in [tex]$75[/tex] 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.

Question

High School

Answer :

sqdancefan sqdancefan · Answer 1 · 2024-07-21T13:55:21-04:00

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.