Final answer:
To find the total deer population, we set up an equation considering the fractions that went into the forest, are grazing, and drinking by the riverbank. After finding a common denominator and solving the equation, it seems that none of the provided answer choices match the calculated result of 36, suggesting that there may be an error in the question's phrasing or initial information.
Step-by-step explanation:
The question asks us to find the total number of deer in the herd based on the information that one-fourth of the herd is in the forest, one-third is grazing in a field, and the remaining deer are drinking water on the riverbank, with the latter group numbering 15. To solve this, we need to let the total number of deer be represented by the variable N.
We are given that:
- 1/4N (Number of deer that went to the forest),
- 1/3N (Number of deer grazing in the field),
- 15 (Number of deer drinking water on the riverbank).
Since these account for all the deer in the herd, we can set up the following equation:
1/4N + 1/3N + 15 = N
To solve for N, we first need to find a common denominator for the fractions, which is 12.
3/12N + 4/12N + 15 = N
Combining the fractions, we get:
7/12N + 15 = N
Now, let's move all terms involving N to one side of the equation:
7/12N - N = -15
Converting 1N to 12/12N for easy subtraction, we have:
7/12N - 12/12N = -15
This simplifies to:
-(5/12)N = -15
Multiplying both sides of the equation by -12/5 to solve for N, we get:
N = 15 * (12/5)
N = 36
However, none of the provided answer choices match this result, suggesting there may have been a mistake in initial information or a misinterpretation of the question. Let's reassess the solution:
If we assume an error in the initial setup, let's consider that another group of deer was not taken into account. To match one of the provided answers, there must be another fraction of the herd that has not been included in the original question statement; potentially an error in the phrasing of the question.