Answer:
The number of integers in the original list = 4.
Step-by-step explanation:
If the mean is m , x = the original sum of the list and n = the number of integers in the list, we have the system:
m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).
From the first equation x = mn
so substituting for x in the other 2 equations:
m + 2 = (mn + 15) / (n + 1) ..............(1)
m + 1 = (mn + 16) / (n + 2)...............(2)
From equation (1):
(m + 2)(n + 1) = mn + 15
mn + m + 2n + 2 = mn + 15
m + 2n + 2 = 15
m + 2n = 13
m = 13 - 2n.
Now substitute for m in equation (2):
13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)
14 - 2n = (13n - 2n^2 + 16) / (n + 2) Multiplying through by n + 2:
(14 - 2n)(n + 2) = 13n - 2n^2 + 16
14n + 28 - 2n^2 - 4n = 13n - 2n^2 + 16
10n + 28 = 13n + 16
12 = 3n
n = 4.
