An odd number between 301 and 370 has three different digits. if the sum of its digits is five times the hundreds digit, find the number. show your work.

The sum of it's digits is 5 times the hundreds digit, which means it must be 15 because 3 has to be the hundreds. Subtract 3 from 15 to get 12, the sum of the other two digits. Both digits must be odd and must be single digits. The number 3 cannot show up in the 2 digits because 3 is already in the hundreds place. That leaves one pair- 5 and 7. It must be 357 because the number must fit between 301 and 370