Question

b. A group of 16 college students went to see the Blue Man Group. Some students had senear the stage that cost $85.00 each and the rest were in the balcony where the seats com$49.50 each. If the total cost for all of 16 tickets came to $969.50, how many seats nearthe stage and balcony seats were purchased?

Answer 1

Given:

Total number of students = 16

Cost of each seat near the stage = $85.00

Cost of each balcony seat = $49.50

Total amount paid = $969.50

Let's find the number of seats near the stage and balcony seats that were purchased.

Let s represent the number of seats near the stage purchased

Let b represent the number of balcony seats.

From this situation, we have the set of equations:

s + b = 16

85s + 49.50b = 969.60

Let's solve the set of equations simultaneously using substitution method to find the values of b and s.

Rewrite the first equation for s:

Subtract b from both sides

s + b - b = 16 - b

s = 16 - b

Substitute (16 - b) for s in the second equation:

85(16 - b) + 49.50b = 969.50

Apply distributive property:

85(16) + 85(-b) + 49.50b = 969.50

1360 - 85b + 49.50b = 969.50

Combine like terms:

1360 - 35.50b = 969.50

Subtract 1360 from both sides:

1360 - 1360 - 35.50b = 969.50 - 1360

-35.50b = -390.50

Divide both sides by -35.50:

`\begin{gathered} (-35.50b)/(-35.50)=(-390.50)/(-35.50) \\ \\ b=11 \end{gathered}`

Substitute 11 for b in either of the equations.

Take equation 1:

s + b = 16

s + 11 = 16

Subtract 11 from both sides:

s + 11 - 11 = 16 - 11

s =