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xenn [34]
3 years ago
13

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

Mathematics
1 answer:
MissTica3 years ago
7 0

Answer:

The two numbers are 1 and 2.

Step-by-step explanation:

Let the two numbers be <em>a </em>and <em>b</em>.

One number is twice another, so let's let <em>b=2a</em>.

Their reciprocals are 3/2. Thus:

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

Substitute and solve for <em>a: </em>

<em />\frac{1}{a}+\frac{1}{2a} =\frac{3}{2}\\<em />

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.

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