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

Answer 1

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

To Find:

Percentage of occupancy

Solution:

Define x:

Ratio of circle seats to stall seats = 2 : 5

Circle seats = 2x

Stall seats = 5x

Solve x:

$\text{Circle seats} = 2x$

$\text{Circle seats} = 528$

$2x = 528$

$x = 528 \div 2$

$x = 264$

Find the number of stall seats:

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

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

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

Find the number of stall seats taken:

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

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

Find the total number of seats taken:

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

$\text{seats taken} = 1056$

Find the percentage of occupancy:

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

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

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

Answer: The occupancy rate is 57.1%