SOLUTION: Elementary and Intermediate Algebra, 3e ISBN: 9780073533490 Page 487 Number 14 For each problem, write a system of equations in two or three variables. Use the method of yo

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Question 168297This question is from textbook Elementary and Intermediate Algebra, 3e
: Elementary and Intermediate Algebra, 3e ISBN: 9780073533490
Page 487 Number 14
For each problem, write a system of equations in two or
three variables. Use the method of your choice to solve each
system.
14. 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? This question is from textbook Elementary and Intermediate Algebra, 3e

Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
lets call the cost of singles s and the cost of doubles d
so:
5s+12d=390....eq 1
9s+10d=412....eq 2
lets eliminate one of the variables by multiplying eq 1 by -9 and eq 2 by 5
-45s-108d=-3510............now add these two together and the s terms are
45s+50d =2060.............eliminated.
_____________________
-58d=-1450
cost of a double
:
now plug in d's value into eq 1 or 2. I chose eq 1
5s+12(25)=390
5s+300=390
5s=90
cost of a single