Question

a theatre has the capacity to seat people across 2 levels, the circle and the Stalls the ratio of the seats in the circle to the stalls is 2:5 last friday the audience occupied all 528 seats in the circle and 2/3 of the stalls work out the percentage of occupancy to 2 significant figures

Answer 1

Answer: 76%

Step-by-step explanation:

So basically 528 represents a full circle and the amount in the circle is 2:5 to that in the stalls.

So you divide 528 by 2 and then multiply it by 5 to get a full stall of 1320

you then add 1320 and 528 to get a full theatre of 1848

to get 2/3 of seats in the stall you divide 1320 by 3 and then multiply it by 2 to get 880.

For 2/3 of the stall and a full circle you add 880 and 528 to get 1408.

You divide the amount of people in the theatre on Friday by the total amount of people which the theatre can hold so 1408 divided by 1848 and you get the percentage of 76%

Answer 2

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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