Question

How do you write the equation for “The sum of 14 and a number is 8 times the number”?

Answer 1

Hint: For this problem we need to find the equation for the given statement. We can observe that there is a one unknown variable in the statement, so we can assume that number as $x$. Now we will consider the first half of the statement which is the sum of $14$ and the number. We will represent this statement mathematically by using the arithmetic operations and symbols. Now we will consider the second the part of the statement which is $8$ times the number. We can also represent this statement mathematically by using the arithmetic operations. Now we will equate both the values to get the required equation.

Complete step-by-step solution:
Given a statement, the sum of $14$ and a number is $8$ times the number.
Let us assume the number as $x$.
Considering the first half of the given statement which is the sum of $14$ and the number. In this statement we have the term sum, so we are going to use the addition symbol in the mathematical representation. Hence the sum of $14$ and the number is represented by $14+x$.
Considering the second half of the given statement which is the $8$ times the number. In this statement we are going to use the multiplication symbol in the mathematical representation. Hence $8$ times the number is represented by $8\times x$.
Considering the whole statement at once then the mathematical representation of the statement will become as
$\begin{align}
  & \Rightarrow 14+x=8\times x \\
 & \Rightarrow 14+x=8x \\
\end{align}$
Hence the required equation is $14+x=8x$.

Note: In this problem we have only used the arithmetical operations addition and multiplication only. There may be chances of having other arithmetical operations like subtraction and division. We can represent the subtraction with the symbol $-$ and division with $\div \text{ or }/$.