AlgebraHardMinimum booths for required seating
Algebra practice question
A restaurant floor has exactly 18 seating units: tables that seat 4 and booths that seat 6. If the floor must seat at least 90 people, what is the minimum number of booths?
Answer: 9
With b booths and (18 − b) tables: 4(18 − b) + 6b ≥ 90, so 72 + 2b ≥ 90 and b ≥ 9.
Common wrong answers
- If you answered 8
- Eight booths seat 48 + 40 = 88 people — short of 90.
- If you answered 10
- Ten booths work but are not the minimum; nine booths already reach exactly 90.
- If you answered 18
- 18 is the total number of units, not the booth minimum.
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