Postage cost and direct proportionality

Postage cost and direct proportionality

Secondary 2
6 marks
TGM Original Questions

Core stretch

A delivery service uses a model in which the postage charge, \(P\) dollars, is directly proportional to the mass, \(w\) grams, of a parcel. There is no fixed charge or rounding to a weight band. A parcel of mass \(600\) g costs \(\$1.50\) to post.

  1. Express \(P\) in terms of \(w\).[2]
  2. Find the mass, in kilograms, of a parcel for which the postage charge is \(\$3.25\).[2]

The service replaces this model with a revised tariff. The table shows three exact charges under the revised tariff.

Mass (g)Postage charge ($)
\(250\)\(1.25\)
\(400\)\(2.00\)
\(900\)\(4.40\)
  1. Is the revised postage charge directly proportional to the mass of a parcel? Justify your answer using the values in the table.[2]

Solution:

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Answer:(a) \(P=\dfrac{w}{400}\) (b) \(1.3\text{ kg}\) (c) No. The charge per gram is not constant.

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