Question

Shelter A has a capacity of 500 beds and is 90% occupied. Shelter B is 60% occupied. The ratio of the occupancy of Shelter A to Shelter B is 15 : 16. How many beds are in Shelter B?
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Answer 1

Shelter A has a capacity of 300 beds and is 80% occupied. This means that the number of beds in Shelter A that would be

80/100 x 300 = 0.8 x 300 = 240 beds.

Let x represent the capacity of Shelter B. Shelter B is 45% occupied. It means that number of beds in Shelter B that would be occupied is

45/100 x x = 0.45 x x = 0.45x beds.

Total occupancy of shelter A and shelter B would be

240 + 0.45x

The ratio of the occupancy of shelter A to shelter B is 16:27

Total ratio of occupancy = 16 + 27 = 43

Therefore

27/43 x (240 + 0.45x) = 0.45x

27(240 + 0.45x) = 0.45x x 43 = 19.35x =

6480 + 12.15x = 19.35x

6480 = 19.35x - 12.15x = 7.2x

x = 6480/7.2 = 900

Answer 2

$\huge\underbrace\mathrm\purple{Answer}$

Shelter A has a capacity of 300 beds and is 80% occupied. This means that the number of beds in Shelter A that would be

80/100 x 300 = 0.8 x 300 = 240 beds.

Let x represent the capacity of Shelter B. Shelter B is 45% occupied. It means that number of beds in Shelter B that would be occupied is

45/100 x x = 0.45 x x = 0.45x beds.

Total occupancy of shelter A and shelter B would be

240 + 0.45x

The ratio of the occupancy of shelter A to shelter B is 16:27

Total ratio of occupancy = 16 + 27 = 43

Therefore

27/43 x (240 + 0.45x) = 0.45x

27(240 + 0.45x) = 0.45x x 43 = 19.35x =

6480 + 12.15x = 19.35x

6480 = 19.35x - 12.15x = 7.2x

x = 6480/7.2 = 900

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