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The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y...

by AAPL » Fri Mar 27, 2020 4:35 am

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The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If x of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?

A. y/R
B. y/(R-x)
C. xy/(R-x)
D. xy/(R(R-x))
E. y/(R(R-x))

OA D
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Re: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y...

by deloitte247 » Sun Mar 29, 2020 12:47 pm
Birthday present costs y dollars
Contribution of each students = $$\frac{y}{R}$$
If x of the students failed to contribute their share, then contribution of the remaining students
=
$$\frac{y}{R-x}$$
The additional number of dollars that each students must contribute in order to pay for the y dollars percent
$$=\frac{y}{R-x}-\frac{y}{R}$$
$$=\frac{yR-y\left(R-x\right)}{R\left(R-x\right)}$$
$$=\frac{yR-yR+yx}{R\left(R-x\right)}$$
$$=\frac{yx}{R\left(R-x\right)}$$ $$=\frac{yx}{R\left(R-x\right)}or\ \frac{xy}{R\left(R-x\right)}$$
$$Answer\ is\ Option\ D$$
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Re: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y...

by Scott@TargetTestPrep » Sat Apr 04, 2020 1:46 pm
AAPL wrote: ↑
Fri Mar 27, 2020 4:35 am
 Princeton Review

The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If x of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?

A. y/R
B. y/(R-x)
C. xy/(R-x)
D. xy/(R(R-x))
E. y/(R(R-x))

OA D
If all students paid, then each student would contribute y/R dollars. If x students fail to pay, then the remaining (R - x) students must still pay the total cost of the present y, so each will now have to contribute y/(R - x) dollars. The difference between these two amounts represents the additional number of dollars that each of the remaining students must pay.

We can create the following expression:

y / (R - x) - y / R

Getting the common denominator R(R - x), we have:

yR / [R(R- x)] - y(R- x) / [R(R-x)]

(yR - yR + xy) / [R(R- x)]

xy / [R(R - x)]

Answer: D

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