Read the answer back
A solved pair is not yet an answer.
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- Courts: candidate (7, 5).
- Both facts hold. 7 and 5 are whole numbers, so it is an answer.
- Boxes: candidate (15/2, 11/2).
- Both facts hold here too. But half a box is not an answer.
The rule
Check both original equations. Answer the question that was asked. Ask if the story can allow the pair.
Example
Two courts hold 12 matches in all. The first court holds 2 more than the second. Let x be the first court's matches and y the second's. So x + y = 12 and x − y = 2. Add them: the y terms cancel, and 2x = 14. So x = 7 and y = 5.
Check: 7 + 5 = 12 and 7 − 5 = 2. The first court holds 7 matches. The second holds 5.
Now take 13 boxes in all. There are 2 more mango boxes than apple boxes. Let x be the mango boxes and y the apple boxes. Then x + y = 13 and x − y = 2. Adding gives 2x = 15. So x = 15/2 and y = 11/2.
Check: 15/2 + 11/2 = 13 and 15/2 − 11/2 = 2. Both equations hold. But a shop cannot pack half a box. The pair of equations has a solution. The story has none.
| Check | What it catches |
|---|---|
| Both original equations | An equation copied wrongly |
| The question that was asked | A bare pair, with no sentence |
| Can the story allow it? | A fraction of a box or a match |