Answer:
<em>An adult ticket costs $4. A child ticket costs $7.</em>
Step-by-step explanation:
We want to find out the price of an adult ticket and the price of a child ticket. The unknowns in this problem are those two prices. Since they are unknown, we will choose a variable to represent each unknown.
Let a = price of one adult ticket
Let c = price of one child ticket
3 adult tickets and 9 child tickets sold for $75.
3 adult tickets cost 3a. 9 child tickets cost 9c. Together they cost 3a + 9c. They cost $75, so our first equation is
3a + 9c = 75
8 adult tickets and 5 child tickets sold for $67.
8 adult tickets cost 8a. 5 child tickets cost 5c. Together they cost 8a + 5c. They cost $67, so our second equation is
8a + 5c = 67
We have a system, of equations:
3a + 9c = 75
8a + 5c = 67
We will use the addition method and cancel out a. Multiply the first equation by -8. Multiply the second equation by 3.
-24a - 72c = -600
24a + 15c = 201
Add the two equations just above.
-57c = -399
c = 7
Now substitute c = 7 in the first original equation and solve for a.
3a + 9c = 75
3a + 9(7) = 75
3a + 63 = 75
3a = 12
a = 4
An adult ticket costs $4. A child ticket costs $7.
