If the average of 5 consecutive integers is 15 then what is the difference between the least and the greatest of the 5 ingers?
Created: 2 years ago |
Updated: 8 months ago
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Let's denote the five consecutive integers as x, x + 1, x + 2, x + 3, and x + 4, where x is the smallest integer among them.
According to the given information, the average of these integers is 15. So, we can write the equation:
(x + x + 1 + x + 2 + x + 3 + x + 4) / 5 = 15
Now, let's simplify this equation:
(5x + 10) / 5 = 15
Now, multiply both sides of the equation by 5 to isolate 5x:
5x + 10 = 15 * 5
5x + 10 = 75
Subtract 10 from both sides:
5x = 75 - 10
5x = 65
Now, divide by 5:
x = 65 / 5
x = 13
So, the smallest integer is 13, and the greatest integer is x + 4 = 13 + 4 = 17.
The difference between the greatest and the least of the 5 integers is:
17 - 13 = 4
Therefore, the difference is 4.
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