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algebraic expressions

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mingshum
Senior Member

USA
29 Posts

Posted - 02/28/2009 : 20:16:00

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.

skeeter
Advanced Member

USA
5634 Posts

Posted - 03/01/2009 : 13:25:59

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)]

mingshum
Senior Member

USA
29 Posts

Posted - 03/01/2009 : 17:47:07

Thank you for your clear explanation laced with humor!

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