SOLUTION: If mean of 100 numbers is 45. The mean that 99 numbers is 44 . What is the first number ?

Algebra.Com
Question 752832: If mean of 100 numbers is 45. The mean that 99 numbers is 44 . What is the first number ?
Answer by Okeke_Christian(26)   (Show Source): You can put this solution on YOUR website!
Formula for Mean (Average) = Sum of all numbers / Total number of numbers


Mean of 100 numbers = Sum of all hundred numbers / 100


We don't know the sum of all hundred numbers, so we call it x.
From the question, mean of 100 numbers is 45. Therefore:

Cross Multiply:

Therefore, the sum of those hundred numbers is 4,500.
Now,
Mean of 99 numbers = Sum of all ninety-nine numbers / 99
We don't know the sum of all ninety-nine numbers, so we call it y.
Mean of 99 numbers is equal to 44 so,

Cross Multiply:

Therefore, the sum of the remaining ninety-nine numbers is 4356.


Do you rememeber that when we had 100 numbers, the sum was 4,500?
When we removed one number, the sum became 4,356. So, what was that number we removed?



144 is the first number!

RELATED QUESTIONS

The arithmetic mean of three numbers is 100. If the mean of the first two numbers is 50, (answered by solver91311)
the arithmetic mean of five numbers is 60. if the arithmetic mean of the first four... (answered by mananth)
The mean of five numbers is 6. If one of the numbers is removed, the mean becomes 7.... (answered by scott8148)
The mean of five numbers is 6. If one of the numbers is removed, the mean becomes 7.... (answered by Edwin McCravy)
What is the arithmetic mean of first eight odd... (answered by josgarithmetic)
What is the arithmetic mean of first ten natural numbers? (answered by Fombitz)
what is the smallest possible value of 5 distinct whole numbers if the mean is... (answered by Alan3354,greenestamps)
The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find... (answered by Theo,greenestamps)
The mean of five numbers is 12 . If the first four numbers are 7,9,10 and 13 , find the... (answered by Cromlix)