SOLUTION: Need the Linear equation answered: The United States Air Force Academy has two sizes of classrooms. The typical classrooms have 24 seats. The engineering classrooms 32 seats

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Question 1084880: Need the Linear equation answered:
The United States Air Force Academy has two sizes of classrooms. The typical classrooms have 24 seats. The engineering classrooms 32 seats. If one wing has 16 classrooms with 424 seats, how many of each classroom does the wing have?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Let T = number of Typical classrooms
and E = number of Engineering classrooms 


T + E = 16           (1)

24T + 32E = 424      (2)



Multiply (1) by 24 and then subtract (2):



   24T + 24E = 384  (1')

-(24T + 32E = 424)  (2) 

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    0T   - 8E   = -40   —>  E=5   —>  T=16-5=11



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Ans:   5 Engineering classrooms and 11 Typical classrooms.

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Check:  5*32 + 11*24  = 160 + 264 = 424 (ok)