Question 205667: If the average of ten consecutive odd integers is 20, what is the average of the last five of those integers? Please show me how to do it.
Found 2 solutions by RAY100, Targetweek:
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! 1st integer,,,n,,,,,,,,,11
2nd integer,,,n+2,,,,,,,13
3rd integer,,,n+4,,,,,,,15,,,,,sum to 75,,,,,avg is 75/5 = 15
4th integer,,,n+6,,,,,,,17
5th integer,,,n+8,,,,,,,19
.
6th integer,,,n+10,,,,,,21
7th integer,,,n+12,,,,,,23
8th integer,,,n+14,,,,,,25,,,,,,sum to 125,,,,,avg is 125/5=25
9th integer,,,n+16,,,,,,27
10th integer,,,n+18,,,,,,29
.
TOTAL,,,,,,,,,10n +90,,,,,,,,,,,,,,,,,,,,,,,,,,,,,sum to 200
.
If (10n +90)/10 =20,,,,,n+9 =20,,,,n=11
.
substitute back in above
Answer by Targetweek(62) (Show Source):
You can put this solution on YOUR website! This one is harder to explain but not hard to do at all
The average of the numbers has to be 20
since they have to be consecutive, half of them have to be greater than twenty and half of them have to be less than twenty
start with the first odd integer >20
which is 21
so now, what number added to 21 will make the average of the two 20
that number is 19
19 + 20 = 40 / 2 = 20
so now we go to the next hightest integer >20
which is 23
so now, what number added to 23 will make the average of the two 20
that number is 17
17 + 23 = 40 / 2 = 20
Do you see the Pattern?
continue this process until you have used 10 numbers
the answer is 11,13,15,17,19,21,23,25,27,29
and 25 is the average of the last 5
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