Farmer's spent on chicken

[mandy0825]

This question came from the new GMATprep software:
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?
1. $37.80
2. 38.50
3. $39.20
4. 39.50
5. 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 you please kindly point out what went wrong here?

The OA explanation is as follows but I can't understand the colored part...
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 be changed to 14=0.8F?
Many thanks!!

[spoorthy]

I guess this is one of those questions which looks simple but very easy to get wrong.
First of all, I got the question wrong too. I thought the answer is $37.8. But the correct amount is 38.50$

The amount spent by the farmer on chicken is 0.4*35 = 14$
Since he got 20% off, 14$ is only 80% of the full price - which means, 14 = F * 0.8 => F = 17.5$ (do the math yourself).

So the total spent by the farmer is 17.5 + (35-14) = 38.5$

Where you went wrong - The assumption that equation b is greater than a by 8% is not right. I am not sure how you came to that conclusion. But hopefully, the explanation above helps. There must have been a typo in the explanation but their answer was right.

[mandy0825]

Thanks, it's very clear now to me that one should get the 40% amount first and then figure out the full price.

However, might you know why can't I put the 80% (20% discount) in the equation in the first place since my "C" represents full price, but rather have to get the 40% portion first and then obtain the before-discount price?
0.8x0.4xC + 0.6G =35 (C for full chicken feed and G for goat feed)

Another quick way suggested by an expert I asked is: 0.4*35/0.8+0.6*35=38.5.

[RonPurewal]

0.8x0.4xC + 0.6G =35 (C for full chicken feed and G for goat feed)

there are two significant problems with this approach.

first of all, you shouldn't have 0.6g; you should have 0.6 times all the money that the farmer spent.
right now, you are taking 60% of the money that the farmer spent on goat feed, which doesn't represent anything in the problem. (as an analogy, if an item is on sale for 75% of regular price at a store, then 75% of the sale price would be a meaningless quantity -- since it's the sale price that is 75% of some other quantity.)

second -- even if you make that substitution, this approach still won't work, because your two terms are inconsistent with each other.
in the first term, you are attempting to work with a variable that represents the entire full-price cost of the feed (as opposed to what the farmer actually paid). in the second term, however, the goat feed is not 60% of the theoretical full-price cost; it's 60% of how much the farmer actually paid.
so, in other words, your first term uses the amount that the farmer would have paid, while your second term uses the amount that the farmer actually did pay. that's not workable.

[mandy0825]

I see! Thanks so much Ron, much appreciated. I'm clear now that my thought process was wrong. The approach should be to take the respective proportions of the total spending and derive the spending on the sub components. I applied the proportion to the sub components -- an inaccurate approach.
thank you very much!

[amit1234]

i donot understand the problem statement.

first it says :A farmer spent $35 on feed for chickens and goats
then it asks:what amount would he have spent on the chicken feed and goat feed combined

isn't the answer $35??

[jnelson0612]

i donot understand the problem statement.

first it says :A farmer spent $35 on feed for chickens and goats
then it asks:what amount would he have spent on the chicken feed and goat feed combined

isn't the answer $35??

Not quite! Let's review the problem again:

"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?"

I bolded the part that's really important:
--40% of the money was spent on chicken feed, which he bought at a 20% discount off the full price
--the rest of the money (60%) was spent on goat feed which he bought at full price.

Then the question says IF the farmer had paid full price for both the chicken and goat feeds, what amount WOULD he have spent on the chicken and goat feed combined?

I hope this helps! :-)

[amit1234]

i donot understand the problem statement.

first it says :A farmer spent $35 on feed for chickens and goats
then it asks:what amount would he have spent on the chicken feed and goat feed combined

isn't the answer $35??

Not quite! Let's review the problem again:

"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?"

I bolded the part that's really important:
--40% of the money was spent on chicken feed, which he bought at a 20% discount off the full price
--the rest of the money (60%) was spent on goat feed which he bought at full price.

Then the question says IF the farmer had paid full price for both the chicken and goat feeds, what amount WOULD he have spent on the chicken and goat feed combined?

I hope this helps! :-)

Thanks. Its quite clear now.

[RonPurewal]

excellent