Skip to main content

2017 AMC 10A Problem 5

Problem 5 of 25EasierAlgebraArithmetic

The sum of two nonzero real numbers is 44 times their product. What is the sum of the reciprocals of the two numbers?

Answer choices

Show solution

Solution

Let xx and yy be the two numbers. We are given that x+y=4xy.x + y = 4xy. Note that 1x+1y=x+yxy=4. \dfrac{1}{x} + \dfrac{1}{y} = \dfrac{x + y}{xy} = 4. Thus, C is the correct answer.
AoPS wiki

Tagged: algebraic manipulation · fraction

More practice