Question

Which systems of inequalities represents the number of apartments to be built

Answer 1

Given that:

- The office building contains 96,000 square feet of space.

- There will be at most 15 one-bedroom units with an area of 800 square feet. The rent of each unit will be $650.

- The remaining units have 1200 square feet of space.

- The remaining units will have two bedrooms. The rent for each unit will be $900.

Let be "x" the number of one-bedroom apartments and "y" the number of two-bedroom apartments.

• The words "at most 15 one-bedroom units" indicates that the number of these apartments will be less than or equal to 15 units:

`x\leq15`

• You know that the remaining units are two-bedroom apartments. And the number of them is greater than or equal to zero. Then, you can set up the second inequality to represent this:

`y\ge0`

• You know the area of each one-bedroom apartment, the area of each two-bedroom apartment, and the total area that the office building contains. The sum of the areas of the apartments must be less than or equal to the total area of the office building.

Then, the inequality that represents this is:

`800x+1200y\leq96,000`

• Therefore, you can set up this System of Inequalities to represent that situation:

`\begin{gathered} \begin{cases}x\leq15 \\ \\ y\ge0 \\ \\ 800x+1200y\leq96,000 \\ \end{cases} \\ \end{gathered}`

Hence, the answer is: Last option.