Question

A theater sold 830 tickets to a concert. Advance tickets sold for $25 each, while tiekets sold at the door were $35 each. The theater took in a total of $23,810 from ticket sales. How many of each type of ticket did they sell?

Answer 1

524 advance tickets and 306 door tickets

Explanation:

To solve, set up a pair of simultaneous equations

let a be number of advance tickets and d the number of door tickets , then

a + d = 830 → (1) [ based on ticket sales ]

25a + 35d = 23810 → (2) [ based on revenue ]

Rearrange (1)

a + d = 830 ( subtract d from each side )

a = 830 - d → (2)

substitute a = 830 - d into (2)

25(830 - d) + 35d = 23810 ( distribute parenthesis on left side and simplify)

20750 - 25d + 35d = 23810

10d + 20750 = 23810 ( subtract 20750 from both sides )

10d = 3060 ( divide both sides by 10 )

d = 306

substitute d = 306 into (2) and solve for a

a = 830 - 306 = 524

Then

524 advance tickets and 306 door tickets were sold