Question

greg, an architect, is designing a hotel in dover. single rooms take up 31 square meters of space and suites take up 75 square meters of space. in total, there are a maximum of 14,800 square meters available. select the inequality in standard form that describes this situation. use the given numbers and the following variables. x = the number of single rooms y = the number of suites 31 + x + 75 + y ≤ 14,800 31x + 75y ≤ 14,800 31 + x + 75 + y ≥ 14,800 31x + 75y ≥ 14,800

Explanation:

Step1: Determine space for single - rooms

Each single room takes 31 square meters and there are $x$ single rooms, so total space for single rooms is $31x$ square meters.

Step2: Determine space for suites

Each suite takes 75 square meters and there are $y$ suites, so total space for suites is $75y$ square meters.

Step3: Set up the inequality

The total available space is 14800 square meters. The combined space of single - rooms and suites cannot exceed this amount. So the inequality is $31x + 75y\leq14800$.

Answer:

$31x + 75y\leq14800$