1. Introduction: When the Question Is a Story
So far you have solved equations that were already written for you. Someone handed you x + 2y = 7 and 2x − y = 4, and your only job was to find x and y.
Real questions almost never arrive like that. They arrive as a story.
"The sum of a father's age and his son's age is 50 years. Six years ago, the father was seven times as old as the son. Find their present ages."
There is not a single x or y in that sentence. No equation. Just words about ages and years. And that is exactly the part that scares most students. You can solve the equations once they exist — but here, you have to build them first.
This lesson is about that one skill: turning a story into a pair of equations. Once the two equations are on paper, you already know what to do — substitution or elimination, the same methods you just learned. The hard part, the new part, is the translation.
Here is the idea. Every word problem you will meet hides exactly two unknown numbers and gives you exactly two facts about them. Your job is to name the unknowns and write each fact as one equation. Two unknowns, two facts, two equations.
Stop scrolling. Try it in your head before reading on. In the father–son story above, what are the two unknown numbers the question is really asking for?
The father's present age and the son's present age. That's it. Everything else in the story — the 50, the "six years ago", the "seven times" — is just clues about those two numbers.
By the end of this lesson you will be able to read a word problem, name the two unknowns, write two clean equations, solve them, and then translate the answer back into the language of the story.