Direct Variation

If a person buys some packets of sugar, the total cost is proportional to the number of packets bought.

The cost of 2 packets at Nx per packet isN2x.

The cost of 3 packets at Nx per packet isN3x.

The cost of n packets at Nx per packet isNnx.

The ratio of total cost to number of packets is the same for any number of packets bought.

This is an example of direct variation,  or direct proportion. The cost, C, varies directly with the number of packets, n. In the second example, the mass, M, varies directly with the length, L.

The symbol ∝ means ’varies with’ or ‘is proportional to’. The statements in the prevous paragraph are written:

C ∝ n

M ∝ L

M ∝ L really means that the ratio M/L is constant (i.e. stays the same).

Example

1 packet of sugar costs x naira. What will be the cost of 20 packets of sugar?

Cost varies directly with the number of packets bought.

Cost of 1 packet  = x naira

Cost of 20 packets = 20 X x naira

= 20x naira

Example

C ∝ n and C = 5 when n = 20. Find the formula connecting C and n.

C ∝ n means C/n = k.

0r C = kn

C = 5 when n = 20

hence  5 = k V 20

k = ¼

Thus, C = ¼n is the formula which connects C and n…

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