At the museum, the o'rourke family bought 3 adult tickets and 2 children's tickets for $23.50. the patel family bought 2 adult tickets and 4 children's tickets for 25. find the cost of each type of ticket.

The adult tickets sell for $5.50 and the child tickets sell for $3.50.

Explanation
The system of equations that describes this is
3a+2c=23.50
2a+4c=25

In order to solve this, we want the coefficients of one of the variables to be the same.  To do this, we will multiply the first equation by 2:
2(3a+2c=23.50)→6a+4c=47

We now have
6a+4c=47
2a+4c=25

We will subtract the two equations:
(6a+4c=47)-(2a+4c=25)
This gives us
4a=22

Divide both sides by 4:
4a/4 = 22/4
a=5.50

Substituting this into the first equation,
3(5.50)+2c=23.50
16.50+2c=23.50

Subtract 16.50 from both sides:
16.50+2c-16.50=23.50-16.50
2c=7

Divide both sides by 2:
2c/2 = 7/2
c=3.50

This means the adult tickets are $5.50 and the child tickets are $3.50.