# The sum of half a number and its reciprocal is the same as 51 divided by the number. How do you find the number?

##### 1 Answer
Jan 25, 2016

Write an equation to represent the situation

#### Explanation:

$\frac{x}{2}$ + $\frac{1}{x}$ = $\frac{51}{x}$

Place on a common denominator:

$\frac{x \left(x\right)}{2 \left(x\right)}$ + $\frac{1 \left(2\right)}{2 \left(x\right)}$ = $\frac{51 \left(2\right)}{2 \left(x\right)}$

Now you can eliminate the denominators and solve the resulting quadratic equation.

${x}^{2}$ + 2 = 102

${x}^{2}$ - 100 = 0

Solve by factoring as a difference of squares.

(x + 10)(x - 10) = 0

x = -10 and 10

The numbers are -10 and 10.

Exercises:

1. A third of a number added to four times the number's reciprocal is equal to half the quotient of 104 and the number.