The following are the ages (years) of 5 people in a room:
12, 19, 21, 19, 20
A person enters the room.
The mean age of the 6 people is now 19.
What is the age of the person who entered the room?

the 6th person is 23

Step-by-step explanation

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

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Work Shown:

We see that one of the legs is unknown. We'll call this 'a'.

The other leg is b = 2, which becomes b^2 = 4

The hypotenuse (always opposite the 90 degree angle) is c = sqrt(58). This turns into c^2 = 58 when you square both sides.

Use the pythagorean theorem to get

a^2+b^2 = c^2

a^2+4 = 58

a^2 = 58-4

a^2 = 54

a = sqrt(54)

a = sqrt(9*6)

a = sqrt(9)*sqrt(6)

a = 3*sqrt(6)