Question

joe is responsible for reserving hotel rooms for a company trip. his company changes plans and increases how many people are going on the trip, so they need at least total rooms. joe had already reserved and paid for rooms, so he needs to reserve additional rooms. he can only reserve rooms in blocks, and each block contains rooms and costs . let represent the number of additional blocks that joe reserves. 1) which inequality describes this scenario?

Answer 1

The inequality that describes this scenario is:

B ≥ 5

Let's represent the number of additional blocks that Joe reserves as 'B'.

Since Joe needs to reserve at least 50 total rooms, we can set up an inequality to represent this requirement:

16 + 8B ≥ 50

This inequality states that the sum of the rooms already reserved (16) and the rooms to be reserved in blocks (8B) must be greater than or equal to 50.

To simplify the inequality, we can subtract 16 from both sides:

8B ≥ 50 - 16

8B ≥ 34

Dividing both sides by 8, we get:

B ≥ 34 ÷ 8

B ≥ 4.25

Since Joe can only reserve rooms in whole blocks, we round up 4.25 to the nearest whole number:

B ≥ 5

Therefore, the inequality that describes this scenario is:

B ≥ 5