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.
- Express \(P\) in terms of \(w\).[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 ($) |
|---|---|
| \(250\) | \(1.25\) |
| \(400\) | \(2.00\) |
| \(900\) | \(4.40\) |
- 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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