An equation is a sentence about numbers. If you can say a story as an equation, you can solve it with the one-step moves from One-Step Equations with Multiplying and Dividing and the topics before it. Use expressions for the parts of the story.
Key idea
(1) Choose a letter for the unknown. (2) Write the story as an equation. (3) Solve it. (4) Check the answer in the story, not just the equation.
Why it works
The equation says the same thing as the story, only in symbols, so any number that makes the equation true also makes the story true. Checking in the story catches the case where the equation was written the wrong way round.
Worked example: Money left
After spending \$18, Kai has \$27 left. How much did Kai have at first?
- Let $m$ be the money at first. Spending 18 leaves 27: $m - 18 = 27$.
- Add 18 to both sides: $m = 45$.
- Check in the story: \$45 − \$18 = \$27 left. Yes.
Answer: \$45
Worked example: Equal rows
84 chairs are set out in 6 equal rows. How many chairs are in each row?
- Let $r$ be the chairs in a row. 6 rows of $r$ make 84: $6r = 84$.
- Divide both sides by 6: $r = 14$.
- Check: 6 rows of 14 is 84 chairs.
Answer: 14 chairs
Worked example: Equal pieces
A rope is cut into 5 equal pieces, each 1.2 meters long. How long was the rope?
- Let $L$ be the rope’s length. Cutting it into 5 equal pieces: $\frac{L}{5} = 1.2$.
- Multiply both sides by 5: $L = 6$.
- Check: $6 \div 5 = 1.2$.
Answer: 6 meters
Common mistake
Choosing the operation from one key word. "Left" in the first story leads to subtraction in the equation, $m - 18 = 27$, but solving it takes addition. If you subtract to get the answer, $27 - 18 = 9$, you get a starting amount smaller than what is left. Quick check: put your answer back into the story and read it.