Problem: The numeral 47 in base a represents the same number as 74 in base b. Assuming that both bases are positive integers, the least possible value for a+b written as a Roman numeral, is
Answer Choices:
A. XIII
B. XV
C. XXI
D. XXIV
E. XVI
Solution:
Both a and b must be greater than 7 and 4a+7=7 b+4∴7 b−4a=3∴(a,b)= (15,9)∴a+b=24= XXIV.