Problem: In a certain scale of notation, the square of 24 is represented by 554. The base of this scale is
Answer Choices:
A. 6
B. 8
C. 12
D. 14
E. 16
Solution:
Let b>5 be the base. Since (24b)2=(2b+4)2=4b2+16b+16 and 554=5b2+5b+4 we must have 5b2+5b+4=4b2+16b+16. Solving for b we get b=−1 or 12.