Question

One number is twice another. The sum of their reciprocals is 3/2 . Find the numbers.

Answer 1

Answer:

The two numbers are 1 and 2.

Step-by-step explanation:

Let the two numbers be a and b.

One number is twice another, so let's let b=2a.

Their reciprocals are 3/2. Thus:

$\frac{1}{a}+\frac{1}{b} =\frac{3}{2}$

Substitute and solve for a:

$\frac{1}{a}+\frac{1}{2a} =\frac{3}{2}$

Combine the fractions by forming a common denominator by multiplying the left term by 2:

$\frac{2}{2a} +\frac{1}{2a}=\frac{3}{2}$

Combine and cross-multiply:

$3/2a=3/2\\6a=6\\a=1\\b=2(1)=2$

Thus, the two numbers are 1 and 2.