2012 AMC 10A Problems/Problem 6
Problem 6
The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?
Solution
Let the two number equal and . From the information given in the problem, two equations can be written:
Therefore,
Replacing with in the equation,
So and would then be
The sum would be =