Problem Solving

BTGmoderatorLU wrote:Source: GMAT Prep

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

The OA is B

He spent 40% (of the $35) on chicken feed.
40% of $35 = $14. So, he spent $14 on chicken feed.

He got a 20% discount on the chicken feed.
In other words, he paid 80% of the original price.
So, let C = original price of chicken feed.
We can write 80% of C = $14
Or we can write 0.8C = $14
Or, even better, (4/5)C = $14

To solve for C, we'll multiply both sides by 5/4 to get: C = (14)(5/4) = 17 1/2
So, the original price of the chicken feed = $17.5

Finally, if the farmer spent $14 (of the original $35) on chicken feed, then he spent the remaining $21 on goat feed (at no discount).

So, without the discount, the farmer would have paid $17.5 + $21 = $38.50

Answer: B

Cheers,
Brent

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

BTGmoderatorLU wrote:Source: GMAT Prep

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

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

The 14 dollars for chicken feed represented the price for the feed at a 20% discount. 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 had paid regular price for both feeds, he would have spent 17.5 + 21 = $38.50.

Answer: B