Tickets for a touring production

Question

Tickets for a touring production of Sweeney Todd cost $90 for orchestra seats and $60 for balcony seats. you purchase nine tickets, some in the orchestra and some in the balcony, for a total cost of $720. How many orchestra tickets and how many balcony tickets were purchased?

Answer 1

Nine tickets were purchased. Let Orchestra be o and balcony be b.

 

o + b = 9 --------- Equation (1)

 

or

 

o = 9 - b  

 

Coast of Orchestra tickets is $90,  balcony tickets is $60, and total cost is $720.

 

90 o + 60 b = 720 ----------- Equation (2)

 

Substitute o = 9 - b into equation (2)

 

90 (9-b) + 60 b = 720 ---------- Distribute and combine like terms

 

810 - 90 b + 60 b = 720

 

810 - 810 - 30 b = 720 - 810 -------- Subtract 810 from both sides

 

- 30 b = - 90 

 

-30 b/-30 = -90/-30 ----------------Divide both sides by -30

 

b = 3.

 

 

Substitute b = 3 into equation (1) and solve for o.

 

 

o + b = 9

 

o + 3 = 9

 

o = 6

 

 

orchestra seats = 6

and $60 for balcony seats = 3.

 

Varify answer by substituting the values into Equation (2)

 

90 o + 60 b = 720

 

90 (6) + 60 (3) = 720

540 + 180 = 720

720 = 720.