How can I figure this out?

Question

Five integers have an average of 69. the median is 83. the mode is 85. the range of the 5 integers is 70. what is the second smallest of the 5 integers?

Answer 1

the average is 69, so the total sum is 69*5 = 345
the median is 83, so two of them must be above and two below that 83.
The mode is 85, implying that the two numbers above 83 must both be 85

so the largest number is 85, and the range is 70, implying that the smallest is 85-70 = 15

so the second number is 345-83-85-85-15 = 77

the numbers are 15,77,83,85,85