Two-seater and five-seater benches
Two-seater and five-seater benches
IP 1
7 marks
The benches in a hall are either \(2\)-seaters or \(5\)-seaters.
- There are \(30\) benches with \(105\) seats altogether. Form and solve a pair of simultaneous equations to find the number of each type of bench.[3]
- Explain why \(30\) benches cannot give exactly \(100\) seats.[2]
- If any number of benches may be used, find how many different combinations of benches give exactly \(100\) seats.[2]
Solution:
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Answer:(a) \(15\) two-seaters and \(15\) five-seaters (b) it requires \(3b=40\), so \(b\) is not a whole number (c) \(11\)
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