Word Problems

1. Introduction: Turning a Story Into an Equation

So far in this chapter you learnt to solve a quadratic equation. You were handed something like $x^2 - 5x + 6 = 0$, and you found the values of $x$ — the roots, the numbers that make the equation true.

But real questions do not arrive like that. Real questions arrive as a story. "A vegetable seller bought some onions. Together they cost ₹90…" Nobody hands you an $x^2$. You have to build it yourself.

That building is the whole skill of this lesson. Reading a situation, deciding what the unknown is, and writing the story as an equation.

Stop scrolling. Try it in your head before reading on. If I say "a number multiplied by 3 more than itself gives 40", can you write that as an equation? Sit with it for a moment.

There is one more thing real questions do that pure equations never do. Sometimes the maths gives you two answers, but only one of them makes sense in real life. A breadth cannot be a negative number. You cannot have a fraction of a goat. We will learn to keep the answer that fits the story and throw away the one that does not.

By the end, you will read a word problem and feel calm — because you will have a fixed set of moves to follow every single time.

You can now say what this lesson is about: changing words into a quadratic equation, solving it, and choosing the answer that the real situation allows.