The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers? (a) 12/35 (b) 1/35 (c) 35/8 (d) 7/32

Solution

Let the two numbers be \(x\) and \(y\). According to the given conditions:

• The sum of the two numbers is \(12\), which means \(x + y = 12\).
• Their product is \(35\), which means \(xy = 35\).

We are asked to find the sum of the reciprocals of these numbers, which is \(\frac{1}{x} + \frac{1}{y}\).

Using the properties of fractions, the sum of the reciprocals can be rewritten as:

\[
\frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy}
\]

Substituting the given values for \(x + y\) and \(xy\), we get:

\[
\frac{x + y}{xy} = \frac{12}{35}
\]

Therefore, the sum of the reciprocals of the two numbers is \(\frac{12}{35}\).

The correct answer is (a) \(\frac{12}{35}\).