Question

Shelter A has a capacity of 300 beds and is 80% occupied. Shelter B is 45% occupied. The ratio of the occupancy of shelter A to shelter B is 16:27. How many beds are in shelter B?

Answer 1

• 900 beds in shelter B

Explanation:

Occupied beds in shelter A:

• 0.8*300 = 240

The ratio of occupancy is 16 : 27.

Let x be the occupied beds in shelter B, then we have the ratio:

• 240/x = 16/27
• x = 240*27/16
• x = 405

405 is the 45% of all beds in shelter B.

Let the total beds in shelter B is y:

• 0.45y = 405
• y = 405/0.45
• y = 900 beds

Answer 2

Answer:there are 900 beds in shelter B

Explanation:

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 × 300 = 0.8 × 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 = 0.45 × 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 × (240 + 0.45x) = 0.45x

27(240 + 0.45x) = 0.45x × 43 = 19.35x

6480 + 12.15x = 19.35x

6480 = 19.35x - 12.15x = 7.2x

x = 6480/7.2 = 900