The seats in a theatre are arranged in three categories, A, B and C. 40% of the seats are in category A and the rest are in category B and C. The number of seals in calegory B is 3/7 of the of seals in calegory C. There are 396 more seats in category A than category B. How many seats are there altogether?

Answer 1

A = 0.4 s
B + C= 0.6 s
B = 3 C/7
A = B + 396
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0.4 s = B + 396 = 3 C/7 + 396
C - 0.6 s =-B = - 3C/7
10C/7 = 0.6 s
C = 0.42 s

0.4 s = 3 (0.42 s) /7 + 396
0.4 s = 3 (0.06 s) + 396
0.4 s - 0.18 s = 396
0.22 s = 396
s = 1800
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check
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A = 0.4 s = 720
the rest = 1800 - 720 = 1080
B = 720 - 396 = 324
C = 7/3 B = 756
the rest = 324 + 756 = 1080 WHEW !