joe is responsible for reserving hotel rooms for a company trip. his company changes plans and increases how…

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 50 total rooms.\njoe had already reserved and paid for 16 rooms, so he needs to reserve additional rooms. he can only reserve rooms in blocks, and each block contains 8 rooms and costs $900.\nlet $b$ represent the number of additional blocks that joe reserves.\n1) which inequality describes this scenario?\nchoose 1 answer:\na $16 + 8bleq50$\nb $16 + 8bgeq50$\nc $16 + bleq50$\nd $16 + bgeq50$\n2) what is the least amount of additional money joe can spend to get the rooms they need?

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 50 total rooms.\njoe had already reserved and paid for 16 rooms, so he needs to reserve additional rooms. he can only reserve rooms in blocks, and each block contains 8 rooms and costs $900.\nlet $b$ represent the number of additional blocks that joe reserves.\n1) which inequality describes this scenario?\nchoose 1 answer:\na $16 + 8bleq50$\nb $16 + 8bgeq50$\nc $16 + bleq50$\nd $16 + bgeq50$\n2) what is the least amount of additional money joe can spend to get the rooms they need?

Answer

Explanation:

Step1: Analyze number - of - rooms relationship

The number of already - reserved rooms is 16. Each block contains 8 rooms and the number of blocks is (B). The total number of rooms needed is at least 50. So the sum of already - reserved rooms and rooms from new blocks should be at least 50. The inequality is (16 + 8B\geq50).

Step2: Solve the inequality for (B)

First, subtract 16 from both sides of (16 + 8B\geq50): [ \begin{align*} 16+8B - 16&\geq50 - 16\ 8B&\geq34 \end{align*} ] Then divide both sides by 8: (B\geq\frac{34}{8}=\frac{17}{4}=4.25). Since (B) represents the number of blocks and must be an integer, the smallest value of (B) is 5.

Step3: Calculate the least additional cost

Each block costs $900. If (B = 5), the least additional cost is (5\times900=$4500).

Answer:

  1. B. (16 + 8B\geq50)
  2. $4500