Half of a herd of Deer are grazing in the field and third fourth of the remaining are playing nearby. the rest 9 are drinking water from the pond. find the number of dear in the herd?

Answer 1

Let the total number of deer in the herd be \( x \).

According to the problem:

• Half of the herd is grazing in the field, which is \( \frac{x}{2} \).
• The remaining deer are \( x - \frac{x}{2} = \frac{x}{2} \).
• Of these remaining deer, three-fourths are playing nearby. So, the number of deer playing is \( \frac{3}{4} \times \frac{x}{2} = \frac{3x}{8} \).
• The rest, which are drinking water from the pond, are \( \frac{x}{2} - \frac{3x}{8} \).

Now, let's simplify \( \frac{x}{2} - \frac{3x}{8} \):

• First, convert \( \frac{x}{2} \) to eighths: \( \frac{x}{2} = \frac{4x}{8} \).
• Now, we have: \[ \frac{4x}{8} - \frac{3x}{8} = \frac{x}{8} \]

According to the problem, the number of deer drinking water is 9: \[ \frac{x}{8} = 9 \]

Now, solve for \( x \): \[ x = 9 \times 8 = 72 \]

Thus, the total number of deer in the herd is \( \boxed{72} \).