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unknown quantities

by naaga » Sat Feb 14, 2009 5:54 am
20. 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)
(B)
(C)
(D)
(E)


folks please explain simple method to tackle this kind of problems

thanks in advance
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by cjb » Sat Feb 14, 2009 6:24 am
Hi naaga, this is an algebra question. You've missed out the answers, but I'll show you how this is done.

Hopefully you can see that if fewer people pay, each has to pay more than if everyone paid? Well, the additional amount to be paid is simply:

Amount with few people paying - amount when everyone pays.

The amount when everyone pays is y/R

The amount when x fewer people pay is y/(R-x)

So the difference is:

(y/(R-x)) - (y/R)

Without seeing the answers, I can't say which one is correct, but in a similar question I have seen before, the expression needed to be changed to have a common denominator:

(y/(R-x)) - (y/R) = (yR - y(R-x)) / (R(R-x))

= y(R-R+x) / R(R-x)

= yx / R(R-x)

Of course, there may other equivalent expressions.
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by roger_michael » Sun Feb 15, 2009 1:10 pm
Whenever I see variables, I try to pick numbers and solve, so you can get a target answer to look for in the answer choices.

So I picked: R= 10, y=$20 and x=2

So originally each student contributed $ 2. If 2 students fail to contribute, the new contribution per student would be $ 2.5 (20/8), so the difference will be $ .5 USD. So the answer to look for when you substitute the values you picked is $ .5.

Hope it helps.
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