Answer:
The number of children who must leave the playground so that only 75% of the remaining children are playing tag is 4 children.
Option (a) is true.
Explanation:
Step 1: Find the total number of children playing tag.
We are given that 85% of the 40 children on the playground are playing tag.
To find the number of children playing tag, we can multiply 40 by 85% (or 0.85).
Number of children playing tag = 40 * 0.85 = 34
Step 2: Find the total number of children not playing tag.
To find the number of children not playing tag, we subtract the number of children playing tag from the total number of children.
Number of children not playing tag = 40 - 34 = 6
Step 3: Find the number of children who must leave the playground.
We want to find the number of children who must leave the playground so that only 75% of the remaining children are playing tag.
Let's assume x children must leave.
Number of children playing tag after x children leave = 34 - x
Total number of remaining children after x children leave = 40 - x
According to the question, 75% of the remaining children are playing tag. So we can set up the following equation:
(34 - x) = 0.75 * (40 - x)
Let's solve this equation to find the value of x.
34 - x = 0.75 * 40 - 0.75 * x
34 - x = 30 - 0.75x
0.25x = 4
x = 4 / 0.25
x = 16
Step 4: Determine the answer.
The number of children who must leave the playground is 16.
Therefore,
Option (a) is true.