Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing nearby.The rest 9 are drinking water from the pond.Find the number of deer in the herd.
9 is 1/4 of 1/2 of the herd
1/8 h = 9
To find the number of deer in the herd, we can follow these steps:
Step 1: Let's assume the total number of deer in the herd is "x".
Step 2: Half of the herd are grazing in the field, which means there are x/2 deer grazing.
Step 3: Now, three-fourths of the remaining deer are playing nearby, which means (1/4) * (x/2) deer are playing. This can be simplified to (x/8) deer.
Step 4: The remaining 9 deer are drinking water from the pond.
So, we have the equation: (x/2) - (x/8) = 9
Now, let's solve the equation to find the value of x.
Step 5: To solve the equation, we need to find a common denominator for (x/2) and (x/8), which is 8.
So, the equation becomes: (4x/8) - (x/8) = 9
Step 6: Combine like terms:
(4x - x)/8 = 9
3x/8 = 9
Step 7: Multiply both sides of the equation by 8 to isolate x:
8 * (3x/8) = 9 * 8
3x = 72
Step 8: Divide both sides of the equation by 3 to solve for x:
(3x)/3 = 72/3
x = 24
Therefore, the number of deer in the herd is 24.