Question

Find the whole number which when decreased by 20 is equal to 69 times the reciprocal of the number.

Answer 1

Hint: We will be using the concept of word problems to make equations with the data given in the problem, then we will be using the method of solving equations in one variable to find the answer.

Complete step-by-step answer:
Now, we let the whole number be x.
Now, we have been given that the whole number when decreased by 20 is equal to 69 times the reciprocal of the number. So, we have according to the question,
$\left( x-20 \right)=\dfrac{69}{x}..........\left( 1 \right)$
Now, we will cross multiply it to get,
$\begin{align}
  & x\left( x-20 \right)=69 \\
 & {{x}^{2}}-20x=69 \\
 & {{x}^{2}}-20x-69=0 \\
\end{align}$
So, now we will factorize it to get,
$\begin{align}
  & {{x}^{2}}-23x+3x-69=0 \\
 & x\left( x-23 \right)+3\left( x-23 \right)=0 \\
 & \left( x+3 \right)\left( x-23 \right)=0 \\
 & x=-3\ or\ x=23 \\
\end{align}$
Since, we have been given that x is the whole number. Therefore, $x=23$ is the answer.

Note: To solve these types of questions it is important to note that we have rejected $x=-3$. Since, we have been given that x is a whole number.