Tickets to a show cost $10 for adults and $5 for children. The show was sold out, and the theatre has 500 seats. If the revenue collected from these ticket sales was $2900, how many adult tickets were sold?
Add up the money collected for each kind of ticket. Since 500 were sold, if there were x adult tickets, then there were 500-x child tickets. So,
10x + 5(500-x) = 2900
To solve this problem, we need to set up a system of equations based on the given information.
Let's say the number of adult tickets sold is 'a' and the number of child tickets sold is 'c'. We know that the total number of tickets sold, regardless of type, is equal to the total number of seats in the theater:
a + c = 500 (equation 1)
We also know that the revenue collected from adult tickets is $10 per ticket, and the revenue collected from child tickets is $5 per ticket. The total revenue collected from ticket sales is $2900. So, we can express the revenue in terms of the number of tickets sold:
10a + 5c = 2900 (equation 2)
Now, we have a system of two equations with two unknowns. We can solve this system using substitution or elimination.
Let's solve using substitution. Solve equation 1 for 'c':
c = 500 - a
Substitute this value for 'c' in equation 2:
10a + 5(500 - a) = 2900
Simplify:
10a + 2500 - 5a = 2900
Combine like terms:
5a + 2500 = 2900
Subtract 2500 from both sides:
5a = 400
Divide both sides by 5:
a = 80
Therefore, the number of adult tickets sold is 80.