Question

3) A Hotel has 260 rooms-some singles and some doubles. The singles cost $35 per night and the doubles cost $60 per night. During a Packers game weekend all rooms were occupied. The sales for the night were $14,000. Johnny wrote the following system but forgot to define the variable with let statements x + y = 260 { 60x + 35y = 14000 a. Use words to write the let statements for Johnny's system: i. Let I= ii. Let y b. Solve Johnny's system

Answer 1

The total number of rooms is given as 260.

If Johnny wrote x + y = 260,

Then that means the single rooms were represented by y while the double rooms were represented by x. We know this because, the next equation shows

60x + 35y = 14000,

That is, x rooms at 60 dollars plus y rooms at 35 dollars equals to a total of 14000 dollars.

Therefore, we can solve Johnny's system of equations as follows;

`\begin{gathered} x+y=260---(1) \\ 60x+35y=14000---(2) \\ \text{From equation (1), let x=260-y} \\ \text{Substitute for the value of x into equation (2)} \\ 60(260-y)+35y=14000 \\ 15600-60y+35y=14000 \\ \text{Collect like terms;} \\ 15600-14000=60y-35y \\ 1600=25y \\ 64=y \\ \text{Next, substitute for the value of y into equation (1)} \\ x+y=260 \\ x+64=260 \\ x=260-64 \\ x=196 \end{gathered}`

That means 64 single rooms were rented out, while 196 double rooms were rented out and that resulted in a total sales of $14,000