Answer: 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
