Solve.
-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 $\frac { 1 } { 182 }$. Find the two numbers.
A) 14,15
B) 13,14
C) 12,13
D) 11,12

Question

Quizplus · Accepted Answer

Let the smaller number be $x$ and the larger number be $x+1$. We are given that $\frac{1}{x} \cdot \frac{1}{x+1} = \frac{1}{182}$. Cross-multiplying gives $182x(x+1) = 1$. Expanding and simplifying gives the quadratic $182x^2 + 182x - 1 = 0$. This factors as $(14x-1)(13x+1) = 0$, so $x=\frac{1}{14}$ or $x=-\frac{1}{13}$. Since $x$ must be positive, we have $x=\frac{1}{14}$ and $x+1=\frac{15}{14}$. Thus the two numbers are 13 and 14, and the answer is $\boxed{	ext{(B)}}$.

Solve -One Number Is One Larger Than Another Positive Number 1182\frac { 1 } { 182 }1821​

Solve
-One Number Is One Larger Than Another Positive Number $\frac { 1 } { 182 }$