Calculate Difference: Average of Numbers
Let the five numbers in decreasing order be \(n_1, n_2, n_3, n_4,\) and \(n_5\). This means \(n_1 > n_2 > n_3 > n_4 > n_5\).
Average of First Four Numbers
The average of the first four numbers (\(n_1, n_2, n_3, n_4\)) is given as 25.
- The sum of these numbers is: \(n_1 + n_2 + n_3 + n_4 = 4 \times 25 = 100\) (Equation 1)
Average of Last Four Numbers
The average of the last four numbers (\(n_2, n_3, n_4, n_5\)) is given as 20.
- The sum of these numbers is: \(n_2 + n_3 + n_4 + n_5 = 4 \times 20 = 80\) (Equation 2)
Difference Between First and Last Number
To find the difference between the first number (\(n_1\)) and the last number (\(n_5\)), we subtract Equation 2 from Equation 1:
$ (n_1 + n_2 + n_3 + n_4) - (n_2 + n_3 + n_4 + n_5) = 100 - 80 $
Simplifying the equation:
$ n_1 - n_5 = 20 $
Therefore, the difference between the first and the last number is 20.
Important Questions from Quick Math
Evaluate $5.29 \bar{8} - 6.29 \bar{8} + 7.29 \bar{8} $
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$29+14\times7\div11-9=?$- The average age of father and elder son is 35 years, the average age of father and younger son is 32 years and the average age of the two sons is 17 years. What is the average age of the father and his two sons?
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