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

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

PS04683

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!!

Bunuel · Accepted Answer

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. $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 have spent 17.5 + 21 = $38.5.

Answer: B.

Hope it's clear.

lamania · Answer

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!

Bunuel · Answer

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.

Alexmsi · Answer

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.

umeshagarwal16 · Answer

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

Posted from my mobile device

Divyadisha · Answer

He spent 40% of 35 on chicken feed, i.e 35*40/100= 14

This $14 was 80% (He got 20% discount), So the actual price without discount was= 14*100/80= 17.5

Amount spent on goat feed= 35-14= 21

Total price without discount= 21+17.5= 38.5

B is the answer

law258 · Answer

We know 60% of $35 was spent on goats, leaving us with $14 spent on chickens.

$14 spent was with discount --> $14 = x-0.20x --> 14 = 0.80x --> x = $17.5 (original price)

$17.5+$21 =  $38.5

ScottTargetTestPrep · Answer

The farmer spent 35 x 0.4 = 14 dollars on feed for chickens and thus 21 dollars on goat feed.

If we let p = the regular price of the chicken feed we can create the equation:

0.8p = 14

p = 14/0.8 = 17.5

Thus, if the farmer paid regular price for both feeds, he would have spent 17.5 + 21 = $38.50.

Answer: B

EMPOWERgmatRichC · Answer

Hi All,

This question is essentially about arithmetic and taking the proper notes. You can go about the math steps in a couple of different ways though - depending on how you 'see' this information.

From the prompt, we know that the farmer spent $35 on feed.... 40% of his money on chicken feed.... and the rest on goat feed. This means that for every dollar he spent, $0.40 was spent on chicken feed and $0.60 was spent on goat feed. With a total of $35 spent, we can easily break down the two totals....

(.4)($35) = $14.00 on chicken feed 
The rest = $35 - $14 = $21 on goat feed

We were also told that the chicken feed was purchased at a 20% discount, which means that the farmer paid 80% of the regular price for that feed.

$14.00 = (.8)(Regular Price) 
$14/.8 = (Regular Price) 
$140/8 = (Regular Price) 
$17.50 = (Regular Price)

We're asked what the price would have been if the farmer had bought both feeds at full price.... $21 + $17.50 = $38.50

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

Basshead · Answer

We're told a farmer spent $35 on feed for chickens and goats

He spent 40% of $35 for chicken feed:

40% of 35 = $14
60% of 35 = $21

He bought the chicken feed for 20% discount; therefore if he purchased the chicken feed at full price he would have spent:

$14 = 0.8x

\frac{14}{0.8} = x

17.5 = x

$17.50 + 21 = $38.50

Answer is B.

DanTheGMATMan · Answer

Straightforward word problem:

https://www.youtube.com/watch?v=9SddbBv61HY

KhayatiK · Answer

is there a structured way / standard framework tht helps interpret the "20% discount" as either : given price (here, rs.14) = 80% of of the cp or given price = 20% discount on the cp , (depending on the question) quickly? i could interpret here tht the rs 14 is representing the 80% portion of the cp , but reaching tht interpretation took time by literally imagining the scenario. and im doing this every time. is there a quicker way ?

Bunuel · Answer

If I correctly interpret what you are saying above, you are basically asking how to quickly see whether the given amount ($14 here) is the discounted price (80%) or the discount itself (20%).

In this question, the wording is “bought at a 20% discount,” so $14 is clearly the amount he actually paid (spent) on chicken feed, not the discount amount. That means $14 is the price after a 20% discount, so it must be 80% of the original price.

Quick rule:
 If the question says “paid/spent $X after a Y% discount,” then $X is (100 - Y)% of the original price.
 For example, paid $40 after a 20% discount means $40 is 80% of the original price, so the original price is $40/0.8 = $50.

If it says “the discount was $X at Y%,” then $X is Y% of the original price.
 For example, the discount was $12 at 20% means the $12 is the discount amount itself, so the original price is $12/0.2 = $60.

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

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