At Stewar farm, the ratio between the number of sheep and the number of horses is 4 : 15. Each horse is fed 110 ounces of horse food per day, and the farm needs a total of 13,200 ounces of horse food per day. What is the number of sheep on the farm?

Introduction / Context:
This question combines a ratio of animals with a daily feed requirement for one type of animal. The feed is given only to horses, whose number we infer from the total feed needed. Once we know the number of horses, we can use the sheep to horses ratio to determine how many sheep are present. This is a standard type of ratio and unit multiplication question.

Given Data / Assumptions:

• Ratio of sheep to horses = 4 : 15.
• Each horse eats 110 ounces of horse food per day.
• Total horse food required per day = 13,200 ounces.
• Sheep are not consuming this particular horse food.
• We need to find the number of sheep.

Concept / Approach:
First, compute how many horses are present by dividing the total daily feed by the feed per horse. This gives the count of horses. Then, using the ratio 4 : 15, we interpret 15 ratio units as the number of horses and 4 ratio units as the number of sheep. By finding the value of one ratio unit, we multiply it by 4 to get the number of sheep. This method keeps the reasoning clearly separated into counting horses and then applying the ratio.

Step-by-Step Solution:
Total daily horse food = 13,200 ounces. Food per horse per day = 110 ounces. Number of horses = 13,200 / 110. Compute: 13,200 / 110 = 120 horses. Sheep : horses = 4 : 15. So 15 ratio parts correspond to 120 horses. Value of one ratio part = 120 / 15 = 8. Sheep correspond to 4 ratio parts, so sheep = 4 * 8 = 32.

Verification / Alternative check:
We can cross check by reconstructing the ratio. If sheep are 32 and horses are 120, the ratio sheep : horses is 32 : 120. Dividing both by 8 gives 4 : 15, which matches the original ratio. The feed per horse times the number of horses is 110 * 120 = 13,200 ounces, which matches the total daily requirement. Both ratio and feed data are satisfied.

Why Other Options Are Wrong:
Values like 36, 44, 52 and 60 do not maintain the exact ratio 4 : 15 when the number of horses is 120. For example, with 36 sheep the ratio to 120 horses would be 3 : 10, not 4 : 15. Only 32 sheep give the correct proportional relationship and satisfy all the numerical conditions.

Common Pitfalls:
Some learners mistakenly use the total 13,200 as if it included food for sheep or mix up which animal count the ratio applies to. Another frequent error is to miscalculate 13,200 / 110 or misinterpret 4 : 15 as horses to sheep instead of sheep to horses. Keeping track of which quantity corresponds to which part of the ratio is essential.

Final Answer:
The number of sheep on the farm is 32.