| If two variables x and y are related by a formula
such as y = a + bx, then y is said to vary
partly as the constant a and partly as x.
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 |
