Given One Quantity, Finding the Other

A linear equation like Ax + By = C has two unknowns, so by itself it describes a whole line of possible pairs (x, y). It can't tell you one specific answer. But the moment you're told what one of the variables equals, that freedom disappears. Plug the known value in, multiply it out, and the equation collapses into a single-variable equation: one unknown, one equation, one answer. That's the whole engine behind this question type, whether the letters stand for x and y or for real things like adult and child tickets.

The mechanism never changes: substitute the given number for its variable, simplify the constant term, then isolate the remaining variable with normal equation-solving moves. In a word problem, read the setup first so you know what each variable counts before you substitute, since the arithmetic is identical but the meaning of the leftover variable is the whole point of the question.

This sits right next to solving systems of equations, where you have two equations and need both to pin down both variables. Here you're handed one of those two pieces of information directly, so only one equation is doing any work. It also connects to reading real-world constraints: not every algebraic solution matches the situation, which is why checking whether an answer makes sense in context matters as much as the algebra that produced it.