Word problems turn into the equations you can already solve: two-step equations and equations with parentheses. The new skill is writing the equation.
Key idea
Name the unknown with a letter. Write the story as an equation, one piece at a time. Solve it, then check the answer in the story, not only in the equation.
Why it works
An equation records what happens in the story, in order. Solving it undoes those steps in reverse. That is exactly what you would do with arithmetic: "take away the fee, then share by the price." The equation and the arithmetic are the same thinking written two ways.
Worked examples
Worked example: A fee plus a price per visit
A climbing gym charges a \$15 fee plus \$8 per visit. Lena has paid \$63. How many visits is that?
- Let $v$ be the number of visits: $8v + 15 = 63$.
- Subtract 15: $8v = 48$. Divide by 8: $v = 6$.
- Arithmetic check: $63 - 15 = 48$ dollars were for visits, and $48 \div 8 = 6$ ✓.
Answer: 6 visits
Worked example: Equal groups
Four friends each buy a ticket and a \$3 snack. Together they spend \$56. How much is one ticket?
- Let $x$ be the ticket price: $4(x + 3) = 56$.
- Divide by 4: $x + 3 = 14$. Subtract 3: $x = 11$.
- Check in the story: each spends $11 + 3 = 14$, and $4 \times 14 = 56$ ✓.
Answer: \$11
Worked example: Perimeter
A rectangle is 14 cm long and its perimeter is 46 cm. How wide is it?
- Let $w$ be the width: $2(14) + 2w = 46$, so $28 + 2w = 46$.
- Subtract 28: $2w = 18$. Divide by 2: $w = 9$.
- Check: $14 + 9 + 14 + 9 = 46$ ✓.
Answer: 9 cm
Watch for amounts that happen once (a fee) and amounts that happen for each one (a price per visit). The ones that repeat get multiplied by the unknown.