The sum of the reciprocals of two numbers is 2. One of the reciprocals is 1/2 greater than the other reciprocal. What are the two numbers?

Question

a) Let a and b represent the two numbers. Write a system that represents this situation. How is this system different from other systems you have solved?

b) Use the equations x=1/a and y=1/b and substitute to rewrite your system in terms of x and y.

c) What are the values for a and b? Explain what you did.

Answer 1

(1/x)+(1/y)=1

1/x = (3/2)*(1/y)

(3/2)(1/y)+1(y) = 1

(3/y)+(2/y)=2

5/y=2

y=5/2 => 1/y=2/5 and 1/x=(3/2)(2/5)=3/5