A scaffolding firm charges a fixed erection fee plus \(\pounds18\) for every day scaffolding stays up on a building site. After 9 days the site manager was ...
Question 1 Report
A scaffolding firm charges a fixed erection fee plus \(\pounds18\) for every day scaffolding stays up on a building site. After 9 days the site manager was billed a total of \(\pounds272\).
- Find the fixed erection fee charged by the company. (3)
- Write down a formula for the total charge, \(C\) pounds, after \(d\) days of hire. (1)
Answer Details
A total charge made up of a fixed fee plus a daily rate is a linear relationship; if the daily part of the bill can be calculated separately, the fixed fee is found by subtracting it from the total amount billed.
- The daily charge for \(9\) days is: \[18 \times 9 = 162\] Subtracting this from the total bill of \(\pounds272\) leaves the fixed erection fee: \[272 - 162 = 110\] The fixed erection fee is \(\pounds110\). [3] (correct daily charge, correct subtraction, correct fee)
- Combining the fixed fee with the daily rate of \(\pounds18\) per day of hire: \[C = 110 + 18d\] [1]
Whenever a bill combines a one-off fee with a repeating daily charge, work out the repeating part first (rate \(\times\) number of days) and subtract it from the total; what remains is always the fixed part.
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