Question

The larger of two numbers is twice the smaller number. The sum of their reciprocals is 1. Find the larger number.

Answer 1

1/x + 1/2x = 1
3x = 2x^2
x = 3/2
2x = 3

check:
1/(3/2) + 1/(3) = 2/3 + 1/3 = 1

Answer 2

Let the larger number be y
hence the smallest number is 0.5y
their sum = y + 0.5y
their recipocal = 1/(y+0.5y)
1/(y+0.5y)=1
2 = 2y + y
2 = 3y
y=2/3
hence the larger number is 2/3

Answer 3

Let the larger number be y
hence the smallest number is 0.5y
their sum = y + 0.5y
their reciprocal = 1/(y+0.5y)
1/(y+0.5y)=1
2 = 2y + y
2 = 3y
y=2/3
hence the larger number is 2/3