One number is one larger than another positive number. If the reciprocal of the smaller number is multiplied by the reciprocal of the larger number, the product is $\frac{1}{30}$. Find the two numbers.
A) 4,5
B) 6,7
C) 5, 6
D) 3,4

Question

Quizplus · Accepted Answer

Let the smaller number be $x$ and the larger number be $x + 1$. The reciprocal of the smaller number is $\frac{1}{x}$ and the reciprocal of the larger number is $\frac{1}{x+1}$. According to the problem, $\frac{1}{x} \cdot \frac{1}{x+1} = \frac{1}{30}$. Solving this equation for $x$ gives $x = 5$, so the numbers are 5 and 6.

One Number Is One Larger Than Another Positive Number 130\frac{1}{30}301​ Find the Two Numbers

One Number Is One Larger Than Another Positive Number $\frac{1}{30}$ Find the Two Numbers