Question 245899: In a movie theatre line, x people are behind Darsh, who is y places in front of Anil. If there are z people in front of Anil, how many people are in the line?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! A sketch of the line would help a lot!
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Start of Line: __________ Anil __________ Darsh ___________:Front of line
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The number of people from the start of the line to Darsh is said to be: x
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The number of people from Anil to Darsh is given: y
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The number of people from Anil to the front of the line is given as: z
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So we can separate the line into 3 segments:
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Start of line to Anil = x - y
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From Anil to Darsh = y
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From Darsh to Front of the line = z - y
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So we add the three segments and get: x-y + y + z-y = x + z - y
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We can check with a concrete example. Assume 10 people in the line behind Anil, 5 between Anil and Darsh, and 5 from Darsh to the front of the line. So there are 22 people in the line: 10+5+5+Anil+Darsh.
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||||||||| Anil ||||| Darsh |||||, where each vertical bar represents a person.
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x = 10 + Anil + 5 = 16
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From Anil to the front of the line is z:
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z = 5 + Darsh + 5 = 11
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We know that y = 5 because that is the number of people we put between Anil and Darsh in our setup.
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So, we have 16 + 11 - 5 = 22, which is the number of people we know are in the line: x + z - y.
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