How Many Seats In Upper Auditorium (Formula?)

[DanOh62]

We Sold 180 Tickets to the School play. (Sold Out Show)
The Upper Auditorium seats were priced at $5 per ticket/seat.
The Lower Auditorium seats were priced at $6 per ticket/seat.
We sold $1,030 dollars worth.
How many seats are in the Upper Auditorium?

By Trial and error I get:

50 Tickets * $5 = $250 (upper)
130 Tickets * $6 = $780 (lower)
--------
$1,030

Answer is: There are 50 seats in the upper autitorium.

Question: Is there a forumla for this equation?

Many thanks!

 

[DanOh62]

How Many Seats In Upper Auditorium (Formula?) -- Answered

Denis...Thank you for the tip.

Hint:
U + L = 180
5U + 6L = 1030

Solve for U = Number of seats in Upper Auditorium

1a. U+L=180
1b. U=(180-L)
1c. 5(180-L) + 6L = 1030
1d. 900-5L+6L=1030
1e. -5L+6L=1030-900
1f. -5L+6L=130
1g. 1L=130
So if L=130 what does U equal?
2a. U+L=180
2b. U+130=180
2b. U=180-130
2c. U=50

Answer: There are 50 seats in the Upper auditorium and 130 seats in the Lower auditorium.


dConfirm/Check: From the original question:

The Upper Auditorium seats were priced at $5 per ticket/seat.
The Lower Auditorium seats were priced at $6 per ticket/seat.
We sold $1,030 dollars worth.
Putting the word problem into formula: 5U + 6L = 1030

$5 * 50 = $ 250
$6 * 130 = $ 780
--------
$1,030 Yahoo!

 

[lookagain]

Solve for U = Number of seats in Upper Auditorium

L = number of seats in Lower Auditorium\(\displaystyle \ \ \ \ \ \ \) <-------- * Don't forget this line. (Define all your variables.)

* Over all, you have an excellent and thorough/detailed presentation, DanOh62.