Final answer:
To find a set of numbers with a median of 10 and a mean of 7, the sum of all numbers must equal the mean multiplied by the set count, and the middle value when arranged in order must be 10. Set A, 5,5,10,15,15, meets both criteria.
Step-by-step explanation:
The student has asked for a set of five positive numbers with a median of 10 and a mean of 7. Since the median is the middle number in an ordered set, one of our numbers must be 10. To balance the mean, the sum of all five numbers should equal 5 times the mean, which is 5 x 7 = 35. The number 10 is already one of our numbers, so the remaining four numbers must sum to 25. A simple way to achieve this is to have two pairs of numbers that are equidistant from 7 (the mean), such as 5 and 9, so that their average is 7. However, since we're looking for a mean of 7 and our largest number is 10 (to achieve the median), we need the remaining numbers to be less than 7 to decrease the overall average.
Therefore, the set A. 5,5,10,15,15 works because (5+5+10+15+15)/5 = 10, which gives us our mean of 7, and the middle value (median) when the numbers are ordered is 10. The reasoning process included understanding the definitions of median and mean, as well as some trial and error with the numbers surrounding the fixed median of 10, all while ensuring that the total sum resulted in the desired mean.