Answer
The rooms with kitchen facilities $=46$.
The rooms without kitchen factilities $=14$.
Work Step by Step
Step 1:- Assume unknown quantities as variables.
Let the rooms with kitchen facilities $=x$.
Let the rooms without kitchen factilities $=y$.
Step 2:- Write system of equations.
The given values are
Total number of rooms $=60$
Total nightly revenue is $= \$5260$
In the equation form
$\Rightarrow x+y=60$ ...... (1)
$\Rightarrow 90x+80y=5260$ ...... (2)
Step 3:- Solve the system of equations.
Multiply the equation (1) by $-80$.
$\Rightarrow -80x-80y=-4800$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 90x+80y-80x-80y=5260-4800$
Simplify.
$\Rightarrow 10x=460$
Divide both sides by $10$.
$\Rightarrow \frac{10x}{10}=\frac{460}{10}$
Simplify.
$\Rightarrow x=46$
Plug the value of $y$ into equation (1).
$\Rightarrow 46+y=60$
Subtract $46$ from both sides.
$\Rightarrow 46+y-46=60-46$
Simplify.
$\Rightarrow y=14$
Step 4:- Check the answers.
Substitute the values of $x$ and $y$ into equation (2).
$\Rightarrow 90(46)+80(14)=5260$
$\Rightarrow 4140+1120=5260$
$\Rightarrow 5260=5260$. True.
