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Question 210780: in a local highschool parking lot, the number of unrestricted parking spaces is 12 more than 7 times the number of spaces reserved for the handicapped. if there are 6452 parking spaces in altogether, how many are set aside for the handicapped?
I need it to have an isolated variable
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! You can use any letters of choice.
I will use U and R.
Let U = unrestricted parking spaces
Let R = spaces reserved for the handicapped
U = 12 + 7R
U + R = 6452
We have a system of linear equations in two variables.
Since we are given U to be 12 + 7R, let's plug that into the other equation and solve for R.
12 + 7R + R = 6452
12 + 8R = 6452
8R = 6452 - 12
8R = 6440
R = 6440/8
R = 805
We just found the spaces reserved for the handicapped.
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We now plug R = 805 into either equation to find U.
I will use U + R = 6452 but you can use the other equation if you so desire.
U + 805 = 6452
U = 6452 - 805
U = 5647
The unrestricted parking spaces is 5647.
The spaces reserved for the handicapped is 805.
Did you follow?
NOTE: If you add 805 + 5647, you will get the total number of parking spaces, which was given to be 6452.
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