Cow–goat equivalence in feed consumption: If 21 goats eat as much as 15 cows (same period and same feed), then how many goats will consume as much as 35 cows under identical conditions?

Introduction / Context:
This unitary proportion problem converts an equivalence of goat-to-cow consumption into a general conversion factor. We then scale the number of cows to find the goat equivalent for a different quantity of cows.

Given Data / Assumptions:

• 21 goats ≡ 15 cows (equal feed over equal time)
• Find goats equivalent to 35 cows
• Consumption ratios are linear and constant.

Concept / Approach:
From 21 goats = 15 cows, 1 cow ≡ 21/15 goats = 7/5 goats. Multiply this equivalence by the target number of cows to obtain the required number of goats.

Step-by-Step Solution:
Goats per cow = 21 / 15 = 7/5 = 1.4Goats for 35 cows = 35 * (7/5) = 35 * 1.4 = 49 goats

Verification / Alternative check:
Proportion method: 21 : 15 = x : 35 → x = (21/15) * 35 = 49, which matches the direct conversion approach.

Why Other Options Are Wrong:
38, 37, 41, and 45 are not proportional to the 7/5 goats-per-cow factor derived from the given equivalence.

Common Pitfalls:
Inverting the ratio by mistake (using 15/21) or using a non-integer rounding when the exact value is an integer here (49).

Final Answer:
49