Question

The sum of a number and 4 times it’s reciprocal is 13/3. Find the number(s).

Answer 1

Let the unknown number be "x"

We will write an algebraic equation from the word problem given. Then we will solve for "x".

Given,

Sum of number (x) and 4 times the reciprocal is 13/3

We can convert it into an algebraic equation:

$x+(4\times\frac{1}{x})=\frac{13}{3}$

Now, let's solve for the unknow, x,

$\begin{gathered} x+(4\times\frac{1}{x})=\frac{13}{3} \\ x+\frac{4}{x}=\frac{13}{3} \\ \frac{x^2+4}{x}=\frac{13}{3} \\ 3(x^2+4)=13\times x \\ 3x^2+12=13x \\ 3x^2-13x+12=0 \\ (x-3)(x-\frac{4}{3})=0 \\ x=3 \\ x=\frac{4}{3} \end{gathered}$

The numbers are

$\begin{gathered} 3 \\ \text{and} \\ \frac{4}{3} \end{gathered}$