Answer:
The price of one senior citizen ticket is $8, and the price of one child ticket is $11.
Step-by-step explanation:
You are looking for two things: the price of a senior citizen ticket and the price of a child ticket.
We need to write two equations using two variables.
Let s = price of 1 senior citizen ticket.
Let c = price of 1 child ticket.
First day of ticket sales:
6 senior citizen tickets, 8 child tickets, total sales of $136
Since s is the price of a senior citizen ticket, 6 tickets cost 6s.
Since c is the price of a child ticket, 8 tickets cost 8c.
The total sales is 6s + 8c.
The total sales is $136, so our first equation is
6s + 8c = 136
Now we do the same for the second day of ticket sales.
6 senior citizen tickets, 9 child tickets, total sales of $147.
Since s is the price of a senior citizen ticket, 6 tickets cost 6s.
Since c is the price of a child ticket, 9 tickets cost 9c.
The total sales is 6s + 9c.
The total sales is $147, so our second equation is
6s + 9c = 147
The system of equations is
6s + 8c = 136
6s + 9c = 147
Multiply both sides of the first equation by -1. Write the second equation below it. Then add the equations.
-6s - 8c = -136
(+) 6s + 9c = 147
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c = 11
c = 11, so the cost of a child ticket is $11.
Now substitute 11 for c in the first equation, and solve for s.
6s + 8c = 136
6s + 8(11) = 136
6s + 88 = 136
6s = 48
s = 8
The price of a senior citizen ticket is $8.
The price of a senior citizen ticket is $8, and the price of a child ticket is $11.
