Question

You are the manager of a hotel. The company has a complex consisting of 50 suites. Each suite is rented at $ 400 per month; however, for every $ 20 more, there will be two less suites. The owner calls you back and informs you that he would like to have $ 20240 per month for the rental of his complex. It asks you to determine the rental price for each suite

Answer 1

We were given the following information:

The company has 50 suites

Each suite is rented at $400 per month

For every $20 more, there will be 2 fewer suites

The owner would like to have $20,240 per month for rentals

The rental price for each suite is calculated as shown below:

`\begin{gathered} Old.Price.per.unit=$400$ \\ Number.of.Units=50 \\ New.Price=400+20x \\ New.Number.of.Units=50-2x \\ Revenue=Price* Number.of.Units \\ Revenue=\mleft(400+20x\mright)\mleft(50-2x\mright)=20,240 \\ Revenue=20,000-800x+1000x-40x^2=20,240 \\ Revenue=20,000+200x-40x^2=20,240 \\ \text{Let's rearrange the equation, we have:} \\ Revenue=-40x^2+200x-20,240+20,000=0 \\ Revenue=-40x^2+200x-240=0 \\ \text{Factor the left side of the equation, we have:} \\ -40(x-2)(x-3)=0 \\ Divide\text{ both sides by ''-40'', we have:} \\ -x^2-2x-3x-6=0 \\ (x-2)(x-3)=0 \\ Set\text{ the factors equal to zero, we have:} \\ x-2=0,x-3=0 \\ x=2,x=3 \\ x=2 \\ New.Price=400+20(2)=400+40=\text{ \$}440 \\ New.Number.of.Units=50-2x=50-2(2)=46units \\ x=3 \\ New.Price=400+20\mleft(3\mright)=400+60=\text{\$}460 \\ New.Number.of.Units=50-2x=50-2(3)=44units \\ \\ \therefore\text{The price of the suite is: \$440 for 46 units } \\ OR \\ \text{\$460 for 44 units} \\ \end{gathered}`

Therefore, each suite is worth $440 for 46 units or $460 for 44 units