Problem:
Real numbers a and b satisfy the equations 3a=81b+2 and 125b=5a−3. What is ab?
Answer Choices:
A. −60
B. −17
C. 9
D. 12
E. 60
Solution:
The given equations are equivalent, respectively, to
3a=34(b+2) and 53b=5a−3
Therefore a=4(b+2) and 3b=a−3. The solution of this system is a=−12 and b=−5, so ab=(E)60.
The problems on this page are the property of the MAA's American Mathematics Competitions