The sum of two numbers is 45. The sum of their quotient and the quotient’s reciprocal is 2.05. What is the product of the two numbers?

Source: mathcontest.olemiss.edu 9/19/2011

**SOLUTION**

Let and be the two numbers.

(1)

(2)

Simplify Eq. (2)

(3)

(4)

Substitute the value of from Eq. (1) and the value of from Eq. (3) into Eq. (4)

**Answer**: 500

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Sorry for the late response. Please see post “Seven Boxes”.