SOLUTION: Ten rooms are rented at rates of $80 and $120 per night. The total collected for the ten rooms is $920. a) Write a system of linear equations whose solution gives the number of e

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Ten rooms are rented at rates of $80 and $120 per night. The total collected for the ten rooms is $920. a) Write a system of linear equations whose solution gives the number of e      Log On


   



Question 938510: Ten rooms are rented at rates of $80 and $120 per night. The total collected for the ten rooms is $920.
a) Write a system of linear equations whose solution gives the number of each type of room rented. Be sure to state what each variable represents.
b) solve the system of equations.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = number of $80/night rooms rented
Let +y+ = number of $120/night rooms rented
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(1) +x+%2B+y+=+10+
(2) +80x+%2B+120y+=+920+
------------------------
(2) +2x+%2B+3y+=+23+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +2x+%2B+3y+=+23+
(1) +-2x+-+2y+=+-20+
----------------------
+y+=+3+
and
(1) +x+%2B+3+=+10+
(1) +x+=+7+
7 of the $80/night rooms are rented
3 of the $120/night rooms are rented
--------------------
check:
(2) +2%2A7+%2B+3%2A3+=+23+
(2) +14+%2B+9+=+23+
(2) +23+=+23+
OK