Question

A theater sells tickets for a concert. Tickets for lower-level seats cost $35 each. Tickets for upper-level seats cost $25 each. The theater sells 350 tickets for $10,250. How many types of each ticket were sold?

Answer 1

The Answer is: Lower Level seats = 150. Upper level seats = 200.

Explanation:

Start with two known equations:

1 - the number of Lower Level times 35 + the number of Upper level times 25 = the total dollar amount of $10,250.

35L + 25u = 10250

The number of both types of tickets = 350

L + u = 350

Solve for u:

u = 350 - L

Substitute and solve for L, Lower level seats:

35L + 25(350 - L) = 10250

35L + 8750 - 25L = 10250

10L + 8750 = 10250

10L = 1500

L = 150

There are 150 Lower Level seats.

u = 350 - L

Subtract to get the number of upper level seats:

u = 200

Proof:

35(150) + 25(200) =

$5,250 + $5,000 = $10,250

Answer 2

Answer: number of lower-level seat tickets =150

number of upper-level seat tickets =200

Explanation:

Let number of lower-level seat tickets be x

Let number of upper-level seat tickets be y

Total number of tickets sold by the theatre = 350

x +y = 350 - - - - - 1

Tickets for lower-level seats cost $35 each.

Tickets for upper-level seats cost $25

Cost of x low-level seat tickets = 35x

Cost of upper-level seat tickets = 25y

Total cost of seat tickets =Lower- level seat tickets + upper-level seat tickets

35x + 25y =10250 - - - - - -2

From equation 1

x = 350 -y

Put x = 350 -y in equation 2

35(350-y) + 25y =10250

12250-35y + 25y = 10250

-10y = 10250 -12250 = -2000

y = 2000/10 = 200

x = 350-y = 350-200= 150