Question

The following are the ages (years) of 5 people in a room:

14, 14, 18, 18, 22
A person enters the room.
The mean age of the 6 people is now 16.
What is the age of the person who entered the room​

Answer 1

Explanation:

✧
`\underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \: O \: N}}} }:`

Let the age of a person who entered the room be ' x '.

✧
`\underline{ \underline{ \large{ \tt{G \: I \: V \: E \: N \: \: D \: A\: T \: A } }}} :`

• 14 , 14 , 18 , 18 , 22 , x

n ( number of observation ) = 6

`\sum` x = 14 + 14 + 18 + 18 + 22 + x = 86 + x

Mean = 16

☯
`\boxed{ \large \tt{Mean \: = ( \sum \: x)/(n) }}`

~Plug the values :

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`\large{ \tt{16 = (86 + x)/(6)}}`

~Apply cross product property :

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`\large{ \tt{86 + x = 16 * 6}}`

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`\large{ \tt{86 + x = 96}}`

Move 86 to right hand side and change it's sign

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`\large{ \tt{x = 96 - 86}}`

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`\boxed{ \large{ \tt{x = 10}}}`

`\large{ \boxed{ \boxed{ \underline{ \large{ \tt{Our \: Final \: Answer : \underline{10}}}}}}}`

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Answer 2

10

Explanation:

14+14+18+18+22=86

6*16=96

96-86=10