Problem Solving

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

We need to determine the following ratio:
(full price)/(actual amount spent).

To determine this ratio, plug in an EASY VALUE for the full price of chicken feed.
Since the chicken feed is discounted by 20% -- the equivalent of 1/5 -- let the regular price of chicken feed = $5.

Then:
After the 1/5 discount, the amount spent on chicken feed = 5 - (1/5)*5 = 4.
Since the amount spent on chicken feed represents 40% -- the equivalent of 4/10 -- of the total amount spent, the total amount spent = $10, while the amount spent on goat feed = $6.
Resulting values:
Full price = (regular chicken feed price) + (regular goat feed price) = 5+6 = 11.
Actual amount spent = (regular chicken feed price) + (regular goat feed price) = 4+6 = 10.
Thus:
(full price)/(actual amount spent) = 11/10.

The resulting ratio implies that the full price is equal to 11/10 of the actual amount spent ($35):
(11/10) * 35 = (11/2) * 7 = 77/2 = 38.5.

The correct answer is B.