One night, a hotel manager rented $15$ single rooms and $36$ double rooms for a total of $3900$ dollars per night. The next night, he rented $27$ single rooms and $30$ double rooms for a total $4120$ dollars per night.
How much does the manager charge for each type of room per night?
I have tried about $5$ different methods of breaking it down and am still confused. If you can break it down or make it simpler for me I would extremely thankful.
On
One way you can do it is by making a system of linear equations: $$15s +36d=3900$$ $$27s +30d=4120$$ where $s$ is single room per night and $d$ is the double room per night, if you stay in a hotel for 5 days you pay 5 times the charge of a room per day. If you try and solve the above system for $s$ and $d$ you will get your answer.
A general strategy for word problems like this is to assign variables that seem reasonable, then capture the facts you are given with equations. Here let $s$ be the rent of a single room and $d$ be the rent of a double room. Each night gives you an equation involving $s$ and $d$. That gives two simultaneous equations in two unknowns.