SOLUTION: When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers

Question 1067468: When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original
list?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
When 15 is appended to a list of integers, the mean is increased by 2.
When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1.
How many integers were in the original list
:
Let n = no. of original integers
let x = average value of these integers
:
"When 15 is appended to a list of integers, the mean is increased by 2."
= x + 2
nx + 15 = (x+2)(n+1)
nx + 15 = nx + x + 2n + 2
subtract nx from both sides
15 = x + 2n + 2
0 = x + 2n + 2 - 15
0 = x + 2n - 13
x = 13 - 2n
:
" When 1 is appended to the enlarged list, the mean of the enlarged list is
decreased by 1. "
= x + 2 - 1
= x + 1
nx + 16 = (x+1)(n+2)
nx + 16 = nx + 2x + n + 2
subtract nx from both sides
16 = 2x + n + 2
0 - 2x + n + 2 -16
0 = 2x + n - 14
n = 14 - 2x
replace x with (13-2n) from the first equation
n = 14 - 2(13-2n)
n = 14 - 26 + 4n
n = -12 + 4n
12 = 4n - n
12 = 3n
n = 12/3
n = 4 integers in the original list
:
:
Confirm this; find x:
x = 13 - 2(4)
x = 5
See if this checks out in the statement
""When 15 is appended to a list of integers, the mean is increased by 2."
= 5 + 2
= 7

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