Translating a sentence into a multi-step equation

In word problems, the sentences are translated into multi-step equations for solving. This process can be best understood using examples given below.

Translate the following sentence into an equation.

The sum of a number divided by 8 and 9 equals 3.

Solution

Step 1:

Let the number be x

Step 2:

‘Number divided by 8’ is $\frac{x}{8}$

Step 3:

The word ‘sum’ points to ‘addition’ or ‘+’ operation. The sum of a number divided by 8 and 9 translates to

$\frac{x}{8} + 9$

Step 4:

The word ‘equals’ translates to ‘=’ sign

So, ‘The sum of a number divided by 8 and 9 equals 3’ translates to

$\frac{x}{8} + 9 = 3$

Translate the following sentence into an equation.

Nine times the difference of a number and 7 equals 4.

Solution

Step 1:

Let the number be x

Step 2:

The word ‘difference’ points to ‘subtraction’ or ‘−’ operation

So, ‘Difference of the number and 7’ is x − 7

Step 3:

The word ‘times’ points to ‘multiplication’ or ‘×’ operation

Nine times the difference of a number and 7 is 9 × (x − 7) or 9(x − 7)

Step 4:

The word ‘equals’ translates to ‘=’ sign

So, ‘Nine times the difference of a number and 7 equals 4’ translates to

9(x − 7) = 4