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.
