Suppose ten distinct, positive integers have a median of $10$. ("Distinct integers" means that no two integers are the same.) What is the smallest the average of those ten integers could be? Explain your answer in complete sentences.
Ok so Let us start with the smallest numbers that some can be...
which is naturally 1,2,3,4,5.
then, we place a ten down, and make the 4 next integers: 11,12,13,14,
calculating the average: 1+2+3+4+5=15