in a room of 100 people, 99% are left handed. How many left handed people have to leave the room in order to bring that percentage down to 98%?
To solve this problem, let's break it down step by step.
Initial Number of Left-Handed People:
Total people in the room = 100
Percentage of left-handed people = 99%
Number of left-handed people = 99% of 100 = 0.99 * 100 = 99
Goal:
We want to reduce the percentage of left-handed people to 98% by having some of them leave the room.
Let's Assume:
x left-handed people leave the room.
After Leaving:
Total number of people left in the room = 100 - x
Number of left-handed people left = 99 - x
Condition for 98% Left-Handed People:
The ratio of left-handed people to the total number of people after x leave should be 98% or 0.98.
So, (99 - x) / (100 - x) = 0.98
Solving for x:
99 - x = 0.98 * (100 - x)
99 - x = 98 - 0.98x
Moving terms around: 99 - 98 = 0.98x - x
1 = 0.98x - x
1 = -0.02x
x = -1 / -0.02
x = 50
So, 50 left-handed people need to leave the room to bring the percentage of left-handed people down to 98%.