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. Joe 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. Let B represent the number of additional blocks that Joe reserves. Which inequality describes this scenario? Choose 1 answer: (A) 16+8B = 50 (C) 16+B = 50

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 50 total rooms. Joe 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. Let B represent the number of additional blocks that Joe reserves. Which inequality describes this scenario? Choose 1 answer: (A) 16+8B <= 50 (B) 16+8B >= 50 (C) 16+B <= 50 (D) 16+B >= 50

Bytelearn · Accepted Answer

Initial Reservation: Joe initially reserved 16 rooms. He needs at least 50 rooms in total. Let B represent the number of additional blocks of 8 rooms that Joe reserves. To find out how many more rooms Joe needs, we subtract the number of rooms he has already reserved from the total number of rooms needed. 50 - 16 = 34 Joe needs at least 34 more rooms.Calculating Additional Rooms: Since each block contains 8 rooms, we multiply the number of blocks, B, by 8 to find out the total number of additional rooms Joe reserves. 8B represents the additional rooms Joe will get by reserving B blocks.Total Number of Rooms: To express the total number of rooms Joe will have after reserving B additional blocks, we add the initial 16 rooms to the product of 8 and B. Total rooms = 16 + 8BInequality Representation: Joe needs at least 50 rooms, so the total number of rooms after reserving B blocks must be greater than or equal to 50. Therefore, the inequality that represents this situation is: 16 + 8B ≥ 50

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