The Sandoval family paid $180 for 2 adult tickets and 3 child tickets to an amusement park. The Martinez family paid $105 for 1 adult and 2 child tickets to the same park. What is the price of a child ticket?

The cost of a child ticket is $30

Step-by-step explanation:

Let's define the variables:

A = price of an adult ticket

C = price of a child ticket

We know that:

"The Sandoval family paid $180 for 2 adult tickets and 3 child tickets to an amusement park."

This means that:

2*A + 3*C = $180

and

"The Martinez family paid $105 for 1 adult and 2 child tickets to the same park."

This means that:

1*A + 2*C = $105

Then we have a system of equations:

2*A + 3*C = $180

1*A + 2*C = $105

To solve this, the first step is to isolate one variable in one of the equations, i will isolate A in the second equation:

A = $105 - 2*C

Now we can replace this in the other equation:

2*($105 - 2*C) + 3*C = $180

Now let's solve this for C, the price of a child ticket.

2*($105 - 2*C) + 3*C = $180

$210 - 4*C + 3*C = $180

$210 - C = $180

-C = $180 - $210

-C = - $30

C = $30

The cost of a child ticket is $30

central angle of a triangle has the same measure as its intercepted arc.

step-by-step explanation: