Maths SolverA word problem is, almost always, an algebra problem with a story attached. The story is the difficult part — not because the algebra underneath is hard, but because translating English into algebra is a specific skill that most maths courses spend almost no time teaching explicitly. Students who can mechanically solve $3x + 5 = 17$ in two seconds will sometimes stare for ten minutes at “Alice is twice as old as Bob” without knowing where to start.
Each article in this section picks one common kind of word problem, walks through the standard translation (English → algebra), and then solves it. The calculator on each page does the algebra for you so you can focus on whether you set the equations up correctly — which is where the real work is.
Articles in this section
-
Age problems, demystified
The standard template (“A is X times as old as B; in N years A will be Y times as old”), how to set up the two equations cleanly, and the small trick that makes “in N years” stop being confusing.
-
Distance, speed, and time
The single relationship $d = v t$ in three forms, the units that catch everyone (mph vs km/h, minutes vs hours), and the two-leg problems (“there and back”) where students set up the wrong equation.
-
Compound interest, with and without continuous compounding
The formula $A = P(1 + r/n)^{nt}$, where each letter comes from, what the limit $n \to \infty$ does to it (and why the answer involves $e$), and a calculator that lets you compare different compounding frequencies side by side.
The general method
Almost every word problem on this page reduces to the same three steps, and getting that pattern into your head is more useful than memorising any single template. First, name the unknowns — literally write down “Let $x$ = Alice’s age now.” Second, write one equation per piece of information the problem gives you; if the problem gives you three facts, you should end up with up to three equations. Third, solve the system using whatever algebra is appropriate — substitution, elimination, or just isolating $x$ if there is only one equation. The hard step is the second one; the third one is what we have calculators for.