SOLUTION: A 1000-seat multiplex is divided into 3 theaters. There are 204 seats in Theater 1, and 108 more seats in Theater 2 than Theater 3. How many seats are in Theater 2? a) 796 b) 45

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Question 287839: A 1000-seat multiplex is divided into 3 theaters. There are 204 seats in Theater 1, and 108 more seats in Theater 2 than Theater 3. How many seats are in Theater 2?
a) 796 b) 452 c) 688 d) 344 e) 542
Answer by Stitch(470) About Me  (Show Source):
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Set-Up
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Let A = # of seats in theater 1
Let B = # of seats in theater 2
Let C = # of seats in theater 3
Equation 1: A++=+204
Equation 2: B+=+108+%2B+C
Equation 3: A+%2B+B+%2B+C+=+1000
Solution:
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We were given that A = 204, And equation 2 is solved for B. You can substitute these values into equation 3.
Equation 3: A+%2B+B+%2B+C+=+1000
204+%2B+%28108+%2B+C%29+%2B+C+=+1000 Simplify
312+%2B+2C+=+1000 Subtract 312 from both sides
2C+=+688 Divide both sides by 2
highlight%28C+=+344%29
Now plug 344 into equation 2 for C.
Equation 2: B+=+108+%2B+C
B+=+108+%2B+344
highlight%28B+=+452%29