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A farmer spent $35 on feed for chickens and goats. He spent

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A farmer spent $35 on feed for chickens and goats. He spent [#permalink] New post 21 Apr 2012, 09:03
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Question Stats:

83% (03:30) correct 17% (01:54) wrong based on 41 sessions
A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?

A. $37.80
B. $38.50
C. $39.20
D. $39.50
E. $40.60

I set up the equation as follows: (C for chicken feed and G for goat feed)
0.8x0.4xC + 0.6G =35---a
0.4C+0.6G=35+?----b
equation b is 8% greater than a so I multiplied 35 by 8%, getting $2.8. Thus, I selected 37.8 but the answer is 38.50.
Q: could anyone please kindly point out what went wrong here?

The OA explanation is as follows but I can't understand the part in bold
0.4($35)=F (full price of chicken feed)
$14=0.8F

$17.5=F
Total paid = 17.5+35(0.6)=38.50
Q: how can 14=F and then change to 14=0.8F?

Many thanks!!
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Re: A farmer spent $35 on feed for chickens and goats. He spent [#permalink] New post 21 Apr 2012, 10:41
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Welcome to GMAT Club. Below is a solution for your question.

A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
A. $37.80
B. $38.50
C. $39.20
D. $39.50
E. $40.60

A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14=$21 on goat feed.

Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$14 --> x=$17.5.

Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 17.5+21=$38.5.

Answer: B.

Hope it's clear.
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Re: A farmer spent $35 on feed for chickens and goats. He spent [#permalink] New post 21 Apr 2012, 14:30
Thank you very much Bunuel. It is clear now and the OA explanation must have a typo then.
However, why can't I put the 80% (20% discount) in the equation in the first place but rather have to get the 40% portion first and then obtain the before-discount price? The right approach makes great sense but if I'm faced with similar questions, I may set up the equation by incorporating all the factors again although that won't lead to the right answer.

thank you for your time!
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Re: A farmer spent $35 on feed for chickens and goats. He spent [#permalink] New post 21 Apr 2012, 14:39
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lamania wrote:
Thank you very much Bunuel. It is clear now and the OA explanation must have a typo then.
However, why can't I put the 80% (20% discount) in the equation in the first place but rather have to get the 40% portion first and then obtain the before-discount price? The right approach makes great sense but if I'm faced with similar questions, I may set up the equation by incorporating all the factors again although that won't lead to the right answer.

thank you for your time!


You can write one equation right away I just broke down the solution into several steps to make it easier. If interested here it is: 0.4*35/0.8+0.6*35=38.5. Notice that you should divide 0.4*35 by 0.8 to get original price and not multiply.
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Re: A farmer spent $35 on feed for chickens and goats. He spent [#permalink] New post 22 Apr 2012, 08:32
As always my question. This questin is quite easy but a lot of work to write and to calculate. I would suggest it is a question between 600 - 700 ? Without a calculator it is very time consuming.
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Re: A farmer spent $35 on feed for chickens and goats. He spent [#permalink] New post 22 Apr 2012, 08:56
guys here is an easier way:
Let the farmer had 100 to spend.
He spent 40 on chickens and 60 on goats.
now actual price of chicken feed without discount
x-20%x=40
0.8x=40 or x=50
So without discount he would have spent 50+60=110
Now 110 for 100
For 35 it is 110/100*35=38.5

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Re: A farmer spent $35 on feed for chickens and goats. He spent   [#permalink] 22 Apr 2012, 08:56
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