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SS1: MATHEMATICS - 2ND TERM

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  • Partial Variation (Meaning, Examples)

What is Partial Variation?

Partial variation exists when a quantity is partly constant and partly varies with another quantity.

For example, when a tailor makes a dress, the total cost depends on two things; first the cost of the material (which is partly constant); secondly the amount of time taken to make the dress (partly varies). This is an example of partial variation i.e. 

\( \scriptsize C = a \: + \: kt \)

Where C is the cost and t is time taken, while “a” and “k” are constants.

Example 5.4.1:

The cost of car service is partly constant and partly varies with the time it takes to do the work. It costs ₦3,500 for a \(\scriptsize 5 \normalsize \frac{1}{2} \! \!\) hours service and ₦2,900 for a 4 hours service.

(a) Find the formula connecting cost, ₦C with time T hours.
(b) Hence find the cost of a \(\scriptsize 7 \normalsize \frac{1}{2} \! \!\)  hours service.

Solution

(a) C = P + Kt

 

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