Step-by-step explanation:
To find the maximum possible sum of medians of three sets (X, Y, and Z), we need to distribute the first 15 multiples of 5 in a way that maximizes the median values in each set.
Let's list the first 15 multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75
To maximize the median values, we can arrange the numbers as follows:
Set X (median = 30):
30, 40, 75, _, _
(We choose the largest numbers for Set X to maximize the median value.)
Set Y (median = 25):
5, 20, 50, 60, _
(We choose the next largest numbers for Set Y to maximize the median value.)
Set Z (median = 15):
10, 15, 25, 35, 45
(We fill the remaining numbers into Set Z.)
Now, let's calculate the sum of the medians for each set:
Sum of medians for Set X = 30 (median)
Sum of medians for Set Y = 25 (median)
Sum of medians for Set Z = 15 (median)
Finally, add the medians of the three sets to get the maximum possible sum:
Maximum possible sum of medians = 30 + 25 + 15 = 70
Therefore, the maximum possible sum of medians of the three sets (X, Y, and Z) is 70.