Problem:
If 53=45M=N60, what is M+N?
Answer Choices:
A. 27
B. 29
C. 45
D. 105
E. 127
Solution:
Note that 45M=53=5.93.9=4527, so M=27. Similarly, N60=53= 5⋅203⋅20=10060, so N=100. The sum M+N=27+100=127.
OR
Note that 45M=53, so M=53⋅45=27. Also N60=53, so 60N=35, and N=35⋅60=100. The sumM+N=27+100=127.
Answer: E.
The problems on this page are the property of the MAA's American Mathematics Competitions