There are six people at a bus stop. Each person is half the age of the next person in line. The mean age of the group is 21. How old is the youngest person?
Let's call the age of the youngest person "x".
According to the problem, the second person in line is twice as old as the youngest person, so their age is 2x.
The third person in line is twice as old as the second person, so their age is 4x.
The fourth person in line is twice as old as the third person, so their age is 8x.
The fifth person in line is twice as old as the fourth person, so their age is 16x.
The sixth person in line is twice as old as the fifth person, so their age is 32x.
To find the mean age of the group, we add up all six ages and divide by 6:
x + 2x + 4x + 8x + 16x + 32x = 63x
63x / 6 = 10.5x
We know that the mean age of the group is 21, so we can set up an equation:
10.5x = 21
Solving for x, we get:
x = 2
Therefore, the youngest person at the bus stop is 2 years old.
Let the age of the youngest person be x. Then the ages of the others will be 2x, 4x, 8x, 16x, and 32x.
The total age would be x + 2x + 4x + 8x + 16x + 32x = 63x. Since there are six people, the mean age is the total age divided by 6 people, which is 21.
So, 63x / 6 = 21
Multiply both sides by 6:
63x = 126
Divide both sides by 63:
x = 2
Therefore, the youngest person is 2 years old.