Same shade of paint?
Paint A mixes 6 cans of blue with 8 cans of white. Paint B mixes 72 cans of blue with 96 cans of white. Will the two paints be the same shade?
Asked: will they be the same shade (yes or no). Is a: Are two ratios proportional?. Answer: Yes: both are 3 blue to 4 white.
| Phrase | Value | Counts | Needed? |
|---|---|---|---|
| “6 cans of blue” | 6 cans | blue in A | yes |
| “8 cans of white” | 8 cans | white in A | yes |
| “72 cans of blue” | 72 cans | blue in B | yes |
| “96 cans of white” | 96 cans | white in B | yes |
| Decision | Concept | Correct | Traps → wrong answer |
|---|---|---|---|
| What kind of question is this? | Recognize the question type | Same shade means the same ratio: a proportion check | — |
| How do the mixes compare? | Scale, don’t add | By ratio | By difference: white minus blue → no |
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 |
|---|---|---|---|---|
| Scale, don’t add | Compares the differences (2 more white vs 24 more white). | no | yes | — |