Final answer:
To find the value of w when the arithmetic mean of 5, 6, 7, 8, and w is 10, calculate the sum of these numbers and subtract the sum of the known values from this total, leading to w = 24.
Step-by-step explanation:
The arithmetic mean of 5, 6, 7, 8, and w is 10, therefore we use the formula for the mean to find the value of w:
mean = (sum of all terms) / (number of terms
10 = (5 + 6 + 7 + 8 + w) / 5
To find the sum of all terms, multiply the mean by the number of terms:
10 * 5 = 50
Now subtract the sum of the known terms from 50 to find w:
50 - (5 + 6 + 7 + 8) = w
50 - 26 = w
w = 24
Therefore, the value of w when the arithmetic mean is 10 is 24.