A building site orders ready-mixed concrete by the lorry load, and a reserve of 3 cubic metres already sits on site before any load arrives. The table shows...
Question 1 Report
A building site orders ready-mixed concrete by the lorry load, and a reserve of 3 cubic metres already sits on site before any load arrives. The table shows the total volume on site for different numbers of loads.
| loads, \(L\) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| volume (\(m^3\)) | 9 | 15 | 21 | 27 |
- Find, from the table above, the gradient of the volume-against-loads relationship. (1)
- Find the equation linking volume, \(V\), and the number of loads, \(L\), in the form \(V = mL + c\). (2)
- Use your equation to work out how many loads are needed to reach 51 cubic metres. (1)
Answer Details
Each lorry load adds a fixed volume of concrete on top of the reserve already on site, so the total volume increases linearly with the number of loads, matching the pattern in the table.
(a) Using 1 load and 2 loads from the table:
\[\frac{15 - 9}{1} = 6\] [1 mark]
(b) The reserve already on site before any load arrives is the \(y\)-intercept, 3 cubic metres, so with gradient 6:
\[V = 6L + 3\] [2 marks]
(c) Substituting \(V = 51\):
\[51 = 6L + 3 \implies 6L = 48 \implies L = 8\] [1 mark]
Exam tip: the "reserve already on site" described in the question is exactly the \(y\)-intercept of the equation, the amount present before any loads (when \(L=0\)); look for this kind of wording to identify the intercept in context.
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