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.

For the answer to the question above,

5x3 (the hundreds digit) = 15

so 3+x+y=15. 15-3=12. x+y=12.

No even number + odd number can be = 12, so both digits must be odd.

That leaves us with 3+3+z=15, 3+3+x = 15 and 3+5+y = 15. 3+1+9 (highest odd digit) = 13 so that is wrong.

3+3+9 = 15, but there is a double digit, so wrong again. 3+5+7=15. 357 is the answer.