<PRE><B>Question 405593</B>
One night the manager of the Sea Breeze Motel rented 5 singles and 12 doubles for a total of $390.
 The next night He rented 9 singles and 10 doubles for a total of $412. 
 What is the rental charge for each type of room?
:
Let s = cost of a single room
Let d = cost of a of double room
;
Write an equation for each night,
:
5s + 12d = 390
9s + 10d = 412
:
Multiply the 1st equation by 9, the 2nd equation by 5, results:
45s + 108d = 3510
45s + 50d =  2060
---------------------subtraction eliminates s, find d
0 = 58d = 1450
d = {{{1450/58}}}
d = $25 for a double room
:
Find s using the 1st equation
5s + 12(25) = 390
5s + 300 = 390
5s = 390 - 300
s = {{{90/5}}}
s = $18 for single
:
Check these values in the 2nd equation:
9(18) + 10(25) =
162 + 250 = 412; confirms our solution of: s = 18; d = 25</PRE>