Fixed charge and per-kilogram rate

Fixed charge and per-kilogram rate

Secondary 2
8 marks
TGM Original Questions

A courier's charge \(C\) dollars for a parcel of mass \(m\) kg is modelled by \(C=c+dm\). A \(3\) kg parcel costs \(\$11\) and an \(8\) kg parcel costs \(\$21\).

  1. Using the given information, write down two equations connecting \(c\) and \(d\).[2]
  2. Solve the equations obtained in (i) to find \(c\) and \(d\).[3]
  3. Find the mass \(k\) of a parcel that costs \(\$29\).[2]
  4. State what the value of \(c\) represents in this model.[1]

Solution:

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Answer:(i) \(11=c+3d,21=c+8d\) (ii) \(c=5,d=2\) (iii) \(k=12\text{ kg}\) (iv) \(\text{fixed charge}\hspace{0.5em}\$5\)

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