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To celebrate a colleague's retirement, the T coworkers in an office ag

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Carcass
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To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink] New post   24 Jan 2022, 10:10
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To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/(T-S)
C. Sx/(T-S)
D. Sx/T(T-S)
E. x(T-S)/T
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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink] New post   24 Jan 2022, 10:18
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Carcass wrote:
To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/(T-S)
C. Sx/(T-S)
D. Sx/T(T-S)
E. x(T-S)/T

The PLAN was for T coworkers to share the cost of lunch, which costs x dollars
So, each coworker was supposed to pay x/T dollars

In REALITY, S coworkers failed to pay, which means the total number of coworkers who are paying = T - S
So, in reality, each of the T - S coworkers had to pay x/(T-S) dollars

So, the ADDITIONAL amount each coworker paid = x/(T-S) - x/T
Check the answer choices..... x/(T-S) - x/T is not among them.

Looks like we need to combine the two fractions by first rewriting them with a common denominator as follows:
x/(T-S) - x/T = (x)(T)/(T-S)(T) - (x)(T-S)/(T-S)(T)
= xT/(T-S)(T) - (xT - xS)/(T-S)(T)
= xS/(T-S)(T)

Answer: D
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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]
24 Jan 2022, 10:18
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