Question

A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/ 18. Find the two integers.

Answer 1

To find the two positive integers, we set up an equation based on the given information and then solve for x. The two integers are 18 and 36.

Step-by-step explanation:

Let's assume that one positive integer is x and the other positive integer is 2x. From the given information, we can set up the equation:

1/x - 1/(2x) = 1/18

To solve this equation, we need to find a common denominator for the fractions. The common denominator in this case is 2x. Multiplying both sides of the equation by 2x gives us:

2 - 1 = (2x)/(18)

Simplifying the equation, we have:

1 = x/18

Multiplying both sides by 18, we find that x = 18. Therefore, the two integers are 18 and 2(18) = 36.

Answer 2

9 and 18

Step-by-step explanation:

Let the integers be a and 2a (since one is twice the other).

The reciprocals are 1/a and 1/(2a) respectively.

Difference means tk subtract.

So we have 1/a-1/(2a)=1/18

Multiply both sides by 18:.

18a/a-18a/(2a)=18a/18

Simplify:

18-9=a

Simplify:

9=a

If a=9, then 2a=18

The integers are 9 and 18.

Test:

1/9-1/18

2/18-1/18

1/18

Golden!