Testing proportion claims about a hall hire charge
Testing proportion claims about a hall hire charge
IP 2
7 marks
A community hall charges a fixed booking fee of \(\$a\) plus \(\$b\) for each hour. The total charge for \(h\) hours is \(\$C\). Hiring the hall for \(3\) hours costs \(\$260\) and hiring it for \(5\) hours costs \(\$380\).
- Explain why \(C\) is not directly proportional to \(h\).[1]
- Find the values of \(a\) and \(b\).[3]
- The manager claims that the average charge per hour, \(\dfrac{C}{h}\), is inversely proportional to \(h\). Using \(h=2\) and \(h=4\), test this claim. Hence write down an expression involving \(\dfrac{C}{h}\) that is inversely proportional to \(h\).[3]
Solution:
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Answer:(a) \(\dfrac{C}{h}\) is not constant (\(\dfrac{260}{3}\ne76\)); a fixed fee is charged (b) \(a=80\), \(b=60\) (c) Claim false (\(200\ne320\)); \(\dfrac{C}{h}-60=\dfrac{80}{h}\)
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