SOLUTION: The average of a list of integers goes up by 2 when 21 is added to the list. If 7 is added to the new list, then the average reduces by 1. How many numbers were there in the origin

Question 974053: The average of a list of integers goes up by 2 when 21 is added to the list. If 7 is added to the new list, then the average reduces by 1. How many numbers were there in the original list?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
x/n = y, where x is the total of integers, n is the number of integers, y is their average, then
(x+21) / (n+1) = (y+2)
(x+21+7) / (n+2) = (y+2-1)
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substitute ny for x and we get
(ny+21) = (n+1)(y+2)
(ny+28) = (n+2)(y+1)
we now have two equations in two unknowns
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solve first equation for y
ny+21 = ny+y+2n+2
y +2n = 19
y = 19-2n
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reduce second equation and then substitute 19-2n for y
ny+28 = ny+2y+n+2
2y+n = 26
substitute for y
2(19-2n)+n = 26
38-4n+n = 26
-3n = -12
n = 4, therefore
There are 4 numbers in the original list

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