Two-Step Equation Word Problems: Examples, Practice and Quiz

Many word problems describe something that happens once (a fee, a starting amount, a coupon) and something that repeats (a price per item, an amount per week). That story turns into a two-step equation, ax + b = c, which you solve by undoing the steps in reverse order.

The plan for every problem

  1. ReadFind what the question asks for.
  2. Name the unknownLet x = that amount.
  3. Write the equationRepeat part, one-time part, total.
  4. Solve in two stepsUndo + or − first, then × or ÷.
  5. CheckPut the answer back into the story.

Spot the three parts

Every problem in this lesson has the same three parts. The words around each number tell you which part it is.

PartWords to look forIn the equation
Goes with xper, each, every, a week, an hour, split equally amongmultiplies or divides x
Happens oncefee, flat charge, already has, starts at, coupon, discountadded or subtracted once
Totalin total, altogether, paid, now has, the bill wasafter the equals sign

Worked examples

Your turn

Practice problem Solved: 0

Goes with xHappens onceTotal
1 · Write the equation
x =

Choose “multiplied” when a number repeats for each one (like 15x), or “divided” when x is split equally (like x ÷ 4).

Common mistakes

  • Putting the one-time amount with x. A $40 setup fee is paid once, so it is + 40, not 40x.
  • Undoing in the wrong order. Undo the + or − first, then the × or ÷. Dividing first means dividing every part.
  • Forgetting the other side. Whatever you do to one side of the equation, do to the other side.
  • Stopping at x = 6. Answer the question in words: “6 months”, then check it in the story.

Algebra word problems