What it does
The hard part of a word problem is not the solving, it is turning the story into equations. This page takes one story at a time and shows the four steps:
- Name the unknowns: what x and y stand for.
- Write two equations: each sentence of the story that gives a fact becomes one equation, with a line saying how.
- Solve by elimination or by substitution, every step with the story’s numbers.
- Answer and check: put the answer back into the story, not just into the equations.
There are five kinds of story: ages (now and in a few years), tickets (two groups paying for adult and child tickets), a boat in a stream (downstream the speeds add, upstream they subtract), a rectangle (length, width and perimeter) and banknotes (how many of each). Press New numbers for a fresh story of the same kind. The second card draws both equations as lines; once all the steps are shown, the point where they cross is marked: it is the answer.
It follows the Class 10 Maths chapter pair of linear equations in two variables (algebraic methods and word problems).
To solve any pair you type in yourself and see the ratio test, use linear pairs. Stories whose equations have a square in them lead on to quadratic explorer.
How to use it
- Pick a story with the buttons and read it.
- Try it on paper first: decide what x and y are and write two equations.
- Choose Elimination or Substitution.
- Press Next step to reveal one step at a time and compare with your working, or Show all. Hide steps starts again.
- Look at the graph: the two lines and, at the end, the crossing point with its coordinates.
Worked example
A boat goes 45 km downstream in 3 hours and 27 km upstream in 3 hours. Let x be the speed of the boat in still water and y the speed of the stream, in km/h.
- Downstream the stream helps: x + y = 45 ÷ 3 = 15. … (1)
- Upstream it holds the boat back: x − y = 27 ÷ 3 = 9. … (2)
- Elimination: add or subtract the equations. Subtracting (2) from (1) gives 2y = 6, so y = 3, and then x = 12.
- Check: downstream 12 + 3 = 15 km/h for 3 hours is 45 km; upstream 12 − 3 = 9 km/h for 3 hours is 27 km. ✓
Tips
- Write what x and y stand for, with units, before anything else.
- Ages: “in n years” adds n to both ages. “n years ago” takes n from both.
- Boats and streams: downstream speed = boat + stream, upstream speed = boat − stream. The same works for planes and wind.
- Always check the answer in the words of the story. A negative age or price means an equation was set up wrongly.
FAQ
Which method should I use? Either works. Substitution is quick when one equation already says x = … or y = …; elimination is quick when the x or y numbers already match.
Why does my equation look different from the page’s? It may be the same equation rearranged or multiplied through. If both your equations give the same answer, they are fine.
Is this from the textbook? No. The stories and numbers are made up for practice and follow the syllabus topics; fibub is not part of NCERT.
Is anything saved? No. Everything is worked out in your browser and nothing is stored or sent.
Where the numbers come from
- Standard method for word problems leading to a pair of linear equations in two variables; the stories and numbers are made up for fibub.
- Checked by solving 1000 stories of each kind back to the whole-number answer they were built from, and against hand-worked stories (a boat going 45 km downstream and 27 km upstream in 3 hours each: 12 km/h and 3 km/h).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.