The Ambassador Theatre on Broadway Introduces Chicago, The Musical!
The Ambassador Theatre is selling 3000 tickets to see the hit Broadway show "Chicago". The orchestra seats cost $100.00 per seat. The mezzanine seats cost $55.00 per seat. The total amount collected at the box office was $175, 800. How many mezzanine seats were sold?
1. First, you need to make your two equations.
Equation # 1:
A. Define your variables
*Let the variable o represent the orchestra seats and the variable m represent the mezzanine seats.*
B. Assign the correct co-efficient to the correct variable.
*Assign the co-efficient 100 to the variable O because the orchestra seats cost $100.00 each.*
*Assign the co-efficient 50 to the variable M because the mezzanine seats cost $55.00 each.*
C. Because the total amount collected at the box office equals $178,700, set the two terms 100(o) and 55(m) equal to the total cost which is $175,800.00. Your first equation should appear like this:
100(o) + 55(m) = 175,800
Equation # 2:
A. The number of orchestra seats plus the number of mezzanine seats must equal the total number of seats in the auditorium which is 5,000. Therefore:
o + m = 3000
2. Now that you have both equations, you must choose one of the three ways to solve the system of equations. For this particular problem, elimination is the best choice.
100(o) + 55(m) = 175, 800
o + m = 3000
1. Mulitiply the second equation by -55 to make the "o" cancel out.
100(o) = 175,800
-55(o) = -165,000
2. Combine the two equations into one.
45(o) = 10,800
0 = 240
3. Substitute the "o" value into the original equation.
100(240) + 55(m) = 175,800
24000 + 55m = 175,800
55m = 151, 800 *Subtract 24,00 from both sides*
m = 2760 *Divide by 55*
Congratulations! You have just won your case!