On the first day of ticket sales the school sold 8 senior citizen tickets and 1 child ticket for a total of $97. The school took in $102 on the second day by selling 6 senior citizen tickets and 4 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

A senior citizen ticket costs $11, and a child ticket costs $9.

Step-by-step explanation:

Let s = price of 1 senior citizen ticket, and let c = price of 1 child ticket.

First day:

8s + c = 97

Second day:

6s + 4c = 102

We have a system of 2 equations in 2 unknowns.

8s + c = 97

6s + 4c = 102

We will use the addition method to solve the system.

Multiply both sides of the first equation by -4. Write the second equation below it and add the equations.

     -32s - 4c = -388

(+)     6s + 4c = 102

      -26s       = -286

Divide both sides by -26.

s = 11

Now substitute s with 11 in the first original equation and solve for c.

8s + c = 97

8(11) + c = 97

88 + c = 97

Subtract 88 from both sides.

c = 9

A senior citizen ticket costs $11, and a child ticket costs $9.

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