Question

Seven times a number is equal to twelve more than 3 times the same number. What is the number?

Answer 1

Hint: Word problems are solved best by analyzing the phrases one by one. The first phrase here is “Seven times a number”, and the second phrase is “Twelve more than 3 times the same ”. Assign any variable to the number in question. Change the phrases into expressions using the variable. Next, change the expressions so formed into an equation and solve the equation to get the final answer.

Complete step by step solution:
The phrases formed from the above question are, “Seven times a number” and “Twelve more than 3 times the same number”. The connecting word in between the two phrases is “is equal to”.

Let us consider that the number is x.

Then the first phrase can be written as, $7x$.

The second phrase can be written as, $12 + 3x$.

According to the question, $7x = 12 + 3x$

Hence the word problem gets converted into a linear equation. The main objective here is to find x.

Solving the above equation,
$
7x - 3x = 12 \\
\Rightarrow 4x = 12 \\
$

Dividing both the sides by 4 we get,
$x = \dfrac{{12}}{4} = 3$

Therefore, the number is 3.

Note: Any equation that can be written in the form of $ax + b = 0$is called a linear equation in one variable. Such equations may have more than one variable as well. The more the variables in an equation implies the same number of solutions for the equation.