Answer:
An adult ticket is $8.00 and a child's ticket is $5.50.
Explanation:
We form a system of 2 equations and solve them.
Let a be the price of adult ticket and c the price of a child's.
2a + 4c = 38 (A)
3a + 3c = 40.5 (B)
Multiply equation A by 3 and equation B by -2:
6a + 12c = 114
-6a - 6c = -81 Adding these 2 equations:
0 + 6c = 33
c = 33/6 = 5.5.
Now we substitute for c in equation A:
2a + 4(5.5) = 38
2a = 38 - 22
2a = 16
a = 6.
Let's now check these results by substitution in equation B:
3a + 3c = 40.5
3(8) + 3(5.5) = 24.0 + 16.5 = 40.5
- so it checks out.