Explanation:
Let's denote the five quantities as A, B, C, D, and E. We know that the average of these five quantities is 6, which we can express as:
(A + B + C + D + E) / 5 = 6
Now, we're given that the average of 3 of these quantities (let's say A, B, and C) is 8:
(A + B + C) / 3 = 8
To find the average of the remaining two numbers (D and E), we can first find their total by subtracting the sum of A, B, and C from the total sum of all five quantities:
(A + B + C + D + E) - (A + B + C) = D + E
Now, we know the total sum of all five quantities is 5 times their average, which is 5 * 6 = 30. So:
30 - (A + B + C) = D + E
Since we already know that (A + B + C) / 3 = 8, we can substitute that in:
30 - 3 * 8 = D + E
30 - 24 = D + E
6 = D + E
Now, to find the average of D and E, we can divide their sum by 2:
(D + E) / 2 = 6 / 2 = 3
So, the average of the remaining two numbers (D and E) is 3.