Question

A theatre has the capacity to seat people across two levels the circle and the stalls the ratio of the number of seats in the circle to the number of seats in the stalls is 2:5 last Friday the audience occupied all 528 seats in the circle and 2/3 of the seats in the stalls work out the percentage of occupancy of the theatre last Friday, the audience occupied all the 528 seats in the circle and 2/3 of the seats in the stalls work out the percentage of the occupancy of the theatre last Friday give your answer in 2 significant figures you must show how you get your answer

Answer 1

Answer:

Given:

Capacity of Circle : Stall = 2 : 5

Number of circle seats taken = 528 (which is all the circle seats)

Fraction of stall seats occupied = 2/5

\begin{lgathered}\\\end{lgathered}

To Find:

Percentage of occupancy

\begin{lgathered}\\\end{lgathered}

Solution:

\begin{lgathered}\\\end{lgathered}

Define x:

Ratio of circle seats to stall seats = 2 : 5

Circle seats = 2x

Stall seats = 5x

\begin{lgathered}\\\end{lgathered}

Solve x:

\text{Circle seats} = 2xCircle seats=2x

\text{Circle seats} = 528Circle seats=528

\begin{lgathered}\\\end{lgathered}

2x = 5282x=528

x = 528 \div 2x=528÷2

x = 264x=264

\begin{lgathered}\\\end{lgathered}

Find the number of stall seats:

\text{Number of stall seats} = 5xNumber of stall seats=5x

\text{Number of stall seats} = 5(264)Number of stall seats=5(264)

\text{Number of stall seats} = 1320Number of stall seats=1320

\begin{lgathered}\\\end{lgathered}

Find the number of stall seats taken:

\text{Number of seats taken } = \dfrac{2}{5} \times 1320Number of seats taken =52×1320

\text{Number of seats taken } =528Number of seats taken =528

\begin{lgathered}\\\end{lgathered}

Find the total number of seats taken:

\text{seats taken} = 528 +528seats taken=528+528

\text{seats taken} = 1056seats taken=1056

\begin{lgathered}\\\end{lgathered}

Find the percentage of occupancy:

\text{Percentage Occupancy} = \dfrac{1056}{528 + 1320} \times 100Percentage Occupancy=528+13201056×100

\text{Percentage Occupancy} = \dfrac{1056}{1848} \times 100Percentage Occupancy=18481056×100

\text{Percentage Occupancy} = 57.1\%Percentage Occupancy=57.1%

\begin{lgathered}\\\end{lgathered}

Answer: The occupancy rate is 57.1%

Step-by-step explanation:

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