Map scale
On a map, 1 inch stands for 25 miles. Two towns are 3.5 inches apart on the map. How far apart are they really?
Asked: how far apart really (miles). Is a: Find the missing value in a proportion. Answer: 87.5 miles.
| Phrase | Value | Counts | Needed? |
|---|---|---|---|
| “1 inch” | 1 inch | map distance | yes |
| “25 miles” | 25 miles | real distance | yes |
| “3.5 inches apart” | 3.5 inches | map distance between the towns | yes |
| Decision | Concept | Correct | Traps → wrong answer |
|---|---|---|---|
| What kind of question is this? | Recognize the question type | Same scale, new distance: a missing value | — |
| Which two quantities go together? | Find the pair that forms the ratio | 25 real miles for each 1 map inch | The scale and the map distance → 50/7 |
| What gets scaled up? | Name the unknown | The 3.5 inches between the towns | — |
| Which way round does the ratio go? | Keep the same order on both sides | Miles over inches on both sides | Inches over miles on one side → 0.14 |
The graph starts at the story. The Extract frame holds the decisions; red dashed arrows leave a decision for each trap and run to the wrong answer it produces. The thick green arrow carries the extracted numbers into the question, drawn exactly as on the question’s own page. Any follow-up step comes after, then the answer in the story’s terms. The legend is at the bottom.
| Trap | Mistake | Leads to | Caught by the answer? | Gives itself away with |
|---|---|---|---|---|
| Find the pair that forms the ratio | Divides the scale by the map distance. | 50/7 | yes | 25 ÷ 3.5 ≈ 7.143 |
| Keep the same order on both sides | Flips one side: inches over miles. | 0.14 | yes | 1 × 3.5 = 3.5, 3.5 ÷ 25 = 0.14 |