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 algebraic expressions
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Senior Member

29 Posts

Posted - 02/28/2009 :  20:16:00  Show Profile  Reply with Quote
To celebrate a colleague's graduation, the m coworkers in an office agreed to contribute equally to a catered lunch that costs a total of y dollars. If p of the coworkers fail to contribute, which of the folloing represents the additional mount, in dollars, that each of of the remaining coworkers must contribute to pay for the lunch?

The answer is py/m(m-p)

I tried to substitute numbers in place of the variables but couldn't come up with the above answer.
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Advanced Member

5634 Posts

Posted - 03/01/2009 :  13:25:59  Show Profile  Reply with Quote
m workers

if all m paid, y/m = cost per worker

but, there are p deadbeats ...

(m - p) payers

y/(m - p) = cost per payer

additional cost is y/(m - p) - y/m

common denominator ...

ym/[m(m - p)] - y(m - p)/[m(m - p)]

[ym - y(m - p)]/[m(m - p)]

[ym - ym + yp]/[m(m - p)]

yp/[m(m - p)]
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Senior Member

29 Posts

Posted - 03/01/2009 :  17:47:07  Show Profile  Reply with Quote
Thank you for your clear explanation laced with humor!
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