What is the average of all positive integers that have three digits when written in base 5, but two digits when written in base 7? Write your answer in base 10.
Base 5 ==(100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 130, 131, 132, 133, 134, 140, 141, 142, 143)- From 25 to 48 in base 10
Base 7==(34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 55, 56, 60, 61, 62, 63, 64, 65, 66)- From 25 to 48 in base 10
Sum[25 to 48] =876
Average =876 / 24 =36.5
