SOLUTION: if the average (arithmetic mean) of 5 consecutive integers is 12. what is sum of the least and greatest of the 5 integers ?

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Question 167392: if the average (arithmetic mean) of 5 consecutive integers is 12. what is sum of the least and greatest of the 5 integers ?
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
let x = first number.
x+1
x+2
x+3
x+4
= the other 4 numbers.
the average = sum of the total divided by 5.
sum of the total is 5x + 10
(5x+10)/ 5 = (x+2)
average is (x+2)
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x+2 = average = 12
subtract 2 from both sides of equation.
x = 10
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first number in series is x = 10
last number in series is x + 4 = 14.
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sum of 10 + 14 = 24.
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to prove answer is correct, substitute 10 for x
x = 10
x+1 = 11
x+2 = 12
x+3 = 13
x+4 = 14
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sum of 10+11+12+13+14 = 60
average = 60 / 5 = 12
smallest number is x = 10
largest number is x + 4 = 14
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answer looks good.
x = 10
x + 4 = 14
sum = 24
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