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Question 887629: the numbered ball in a certain jar have an average of 12. if ball 28 is removed from the jar, then the average is decreased by 2. how many balls are there originally?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! not sure if this is right but i did get an answer.
let's see if it makes any sense.
s = sum of numbers on the balls in the jar.
n = number of balls in the jar.
s/n = 12
if the ball with the number 28 on it is removed from the jar, then the average is decreased by 2.
s-28 = sum of numbers on the balls in the jar after the ball with number 28 on it has been removed.
n-1 = number of balls in the jar after the ball with the number 28 on it has been removed.
you get:
(s-28) / (n-1) = (12-2) which results in:
(s-28) / (n-1) = 10
you have 2 equations to work with.
they are:
s/n = 12
(s-28)/(n-1) = 10
in the first equation, solve for s to get s = 12*n
in the second equation, replace s with 12*n to get:
(s-28)/(n-1) = 10 becomes:
(12*n-28) / (n-1) = 10
multiply both sides of this equation by (n-1) to get:
12*n-28 = 10*(n-1)
simplify to get:
12*n-28 = 10*n - 10
add 28 to both sides of this equation to get:
12*n = 10*n - 10 + 28
simplify to get:
12*n = 10*n + 18
subtract 10*n from both sides of this equation to get:
2*n = 18
divide both sides of this equation by 2 to get:
n = 9
that should be your answer.
since s/n = 12 and n = 9, then s/9 = 12 which makes s = 12*9 = 108
the average is 108 / 9 = 12.
now take 28 away from the sum and take 1 away from n and you get s-28 = 80 and n-1 = 8.
the new average is 80/8 = 10
looks like the answer is correct as far as i can see.
there are 9 balls in the jar originally.
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