SOLUTION: There are 3 types of people. A people, B people, and C people. If the total number of A and B people is 30, the total number of B and C people is 45, and the total number of A and
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-> SOLUTION: There are 3 types of people. A people, B people, and C people. If the total number of A and B people is 30, the total number of B and C people is 45, and the total number of A and
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Question 1101401: There are 3 types of people. A people, B people, and C people. If the total number of A and B people is 30, the total number of B and C people is 45, and the total number of A and C people is 35, what is the total amount of people present. Answer by math_helper(2461) (Show Source):
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This problem translates to 3 equations in 3 unknowns:
A+B = 30 (1)
B+C = 45 (2)
A+C = 35 (3)
(2) ==> B = 45-C
Substitute this into (1):
A+(45-C) = 30
A-C = -15
Add this last eqn to (3):
2A = 20
A = 10 —> C = 25 —> B = 20
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Ans: A=10, B=20, and C=25
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Check:
A+B = 10+20 = 30 (ok)
B+C = 20+25 = 45 (ok)
A+C = 10+25 = 35 (ok)
