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# A silo is filled to capacity with W pounds of wheat. Rats eat r pounds

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Math Expert
Joined: 02 Sep 2009
Posts: 45429
A silo is filled to capacity with W pounds of wheat. Rats eat r pounds [#permalink]

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29 Oct 2017, 01:32
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A silo is filled to capacity with W pounds of wheat. Rats eat r pounds a day. After 25 days, what percentage of the silo’s capacity have the rats eaten?

A. 25r/W

B. 25r/(100W)

C. 2,500r/W

D. r/W

E. r/(25W)

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A silo is filled to capacity with W pounds of wheat. Rats eat r pounds [#permalink]

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29 Oct 2017, 08:41
Bunuel wrote:
A silo is filled to capacity with W pounds of wheat. Rats eat r pounds a day. After 25 days, what percentage of the silo’s capacity have the rats eaten?

A. 25r/W

B. 25r/(100W)

C. 2,500r/W

D. r/W

E. r/(25W)

Algebra

The silo is full of wheat.
Capacity is W pounds ("lbs")

Rats eat r lbs per day * 25 days = 25r lbs eaten, are gone

Percentage of the silo's capacity that the rats have eaten:

$$\frac{AmtGone}{AmtFull} * 100=\frac{25r}{W} * 100 =\frac{2,500r}{W}$$

Pick smart numbers

Let full capacity, W = 100 lbs
Let the rats eat r = 1 lb per day

The rats eat 1 lb * 25 days = 25 lbs

They have eaten 25 of the 100 pounds of the silo's capacity.
Percentage of capacity that the rats have eaten:

$$(\frac{part}{whole}) * 100 =\frac{25}{100} * 100 =$$ 25

With W = 100 and r = 1, find the answer choice that yields 25. "Percentage" is included in the prompt. Look for 25 only.

Eliminate B, D, and E immediately. Their denominators are huge.

Between A and C - the question ask for percentage, not the decimal representation of percentage.

A) 25r/W = 25/100 = .25

C) 2500r/W = 2500/100 = 25
That's a match.

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A silo is filled to capacity with W pounds of wheat. Rats eat r pounds   [#permalink] 29 Oct 2017, 08:41
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