A rectangular table seats 10, a round table seats 5. Every table in the restaurant was full. There were MORE THAN 10 and FEWER THAN 15 of each type. 205 customers were seated. How many rectangular and round tables were there altogether?
10 × rectangular + 5 × round = 205. Dividing everything by 5:
Try each one — this is a SHORT list, so testing every value is faster than solving two unknowns at once:
| rectangular | round = 41 − 2×rect | in range 11–14? |
|---|---|---|
| 11 | 19 | ✗ too many |
| 12 | 17 | ✗ too many |
| 13 | 15 | ✗ not LESS than 15 |
| 14 | 13 | ✓ fits! |
14 rectangular + 13 round = 27 tables.
The trap: reading "more than 10 and less than 15" as INCLUDING 10 and 15, or finding one pair that makes 205 without checking that BOTH counts sit inside the range.