Writing Algebraic Expressions

The algebra in these problems is usually easy: add, multiply, divide. The expensive part is translation. Every phrase has a verb that tells you the operation and an order that tells you what goes where. 'Times' and 'more than' usually read in the same order you hear them, but 'less than' flips. Get the order wrong and the whole answer is wrong even though your arithmetic is fine.

The fix is to find the operation word first, then ask which quantity is doing the action to which. 'X more than y' means y + x. 'X less than y' means y - x, not x - y, because the amount 'less' is the one being removed from the other. 'Times' just multiplies in either order since multiplication doesn't care about order, so that one is safe. Once the phrase is correctly translated, you build the full expression piece by piece: a fixed cost stays a plain number, a cost that depends on an amount gets multiplied by a variable, and separate pieces that both apply get added.

This skill sits right before multi-step rate and cost problems. Once you can write the expression, the next move is almost always to plug in a number, solve for a variable, or work backward from a total, like figuring out how many hours a budget buys. The expression is the setup; everything after it is routine arithmetic, so a clean, correctly ordered expression is what makes the rest of the problem painless.