Year 10 Interactive Maths - Second Edition

Part Variation

For example, if a taxi is hired, then the cost of travelling from one place to another may be considered as the sum of two quantities, of which one is constant and the other varies directly as the time taken to reach the destination. That is:

Note:

A part variation keeps a direct variation but includes an extra fixed constant.

Graphically, this relation takes the shape of a straight line with gradient equal to the value of b and the vertical intercept equal to the value of a.

Example 13

The cost, c, of publishing a bulletin consists of two parts:

• a fixed charge, a, of $15; and
• a charge for publishing and the paper, proportional to the number of copies published, n.

If the cost of 500 copies is $35, find the cost of 1000 copies.

Solution:

This is the required formula.

Key Terms

part variation