The average of 5 consecutive whole numbers is 9. Then 1 is subtracted from the first number, 2 is subtracted from the second number, 3 is subtracted from the third number, and so on. What is the average of the five new numbers? Use a variable n to solve.
Let's call the first number in the original set of numbers "n". The second number would be n+1, the third number would be n+2, and so on. Since we know that the average of these 5 consecutive numbers is 9, we can find their sum by multiplying the average, 9, by the number of terms, 5. So the sum of the original set of numbers is 9 * 5 = 45.
Now, we are subtracting 1 from the first number, 2 from the second number, 3 from the third number, and so on. So the first new number would be n - 1, the second new number would be n+1 - 2 = n - 1, the third new number would be n+2 - 3 = n - 1, and so on.
The sum of the new set of numbers can be found by adding up these new numbers. (n-1) + (n-1) + (n-1) + (n-1) + (n-1) = 5n - 5.
Since we know that the sum of these new numbers is 5n - 5, and the number of terms is still 5, we can find the average by dividing the sum by the number of terms. The average of the new set of numbers is (5n - 5) / 5 = n - 1.
Therefore, the average of the five new numbers is n - 1.