Write an Equation From a Word Problem

1) Identify the unknown

Read the word problem carefully and decide what quantity you are trying to find. Let a variable represent that unknown, such as (x) or (n). If the problem mentions another quantity in relation to the unknown, write that relation in words first.

2) Turn words into an equation

Look for key relationships:

• sum / more than / increased by → addition
• difference / less than / fewer than → subtraction
• times / product / twice / triple → multiplication
• equals / is / gives → the equation sign

Translate the statement step by step, keeping the meaning of the sentence. If there is a total, part-whole relationship, or comparison, make sure both sides of the equation represent the same quantity.

3) Simplify if needed

If the equation contains expressions on one side, combine like terms or simplify numbers before solving. The instruction asks for the final answer to be simplified, so write the equation in its cleanest form.

4) Check your equation

Substitute the meaning of the variable back into the equation and see whether both sides match the original story. A good check is to ask: “Does my equation represent the situation exactly?” If not, revisit the wording and adjust the operations or order of the terms.