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?

The youngest person is 2 years old

Step-by-step explanation:

There are six people at a bus stop.

We are told that:

The mean age of the group is 21.

The total number of people is 6 people

Hence:

The total sum of their ages is 21 × 6

= 126

Each person is half the age of the next person in line.

Let the age of the first person be = x

The age of the second person = x/2

The age of the third person = x/2 ÷ 2 = x/2 × 1/2 = x/4

The age of the fourth person = x/4 ÷ 2

x/4 × 1/2 = x/8

The age of the fifth person = x/8 ÷ 2

x/8 × 1/2 = x/16

The age of the sixth person = x/16 ÷ 2

x/16 × 1/2 = x/32

Hence:

x + x/ 2 + x/4 + x/8 + x/16 + x/32 = 126

Lowest Common Denominator is 32

32x + 16x + 8x + 4x + 2x + x/32 = 126

63x /32 = 126

Cross Multiply

63x = 126 × 32

63x = 4032

x = 4032 /63

x = 64 years

Hence, the age of the first person is 64 years.

The age of the youngest person which is the sixth person is :

x/32

= 64/32

= 2 years

step-by-step explanation:

0

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

    -7                           -7

2x is greater than 10

divide by 2 each side

x is greater than 5