DIRECT VARIATION
In direct variation, a change in one quantity ( independent variable ) causes a change in another quantity ( independent variable ) such that the ratio of the two values of the first is the same as the ratio of the corresponding two values of the second. The multiplying ratio is the inverse of this ratio.
In the example we have considered, the more the number of bottles, the more is the cost also, the less the number of bottles, the less is the cost. Also, the less the number of bottles, the less is the cost. In other words, an increase in one quantity (the number) causes an increase in the other quantity (the cost), and a decrease in one quantity causes a decrease in the other quantity. We express this as the cost of the bottles varies directly as the number of bottles.
In general, two quantities x & y are said to vary directly or be in direct variation or in direct proportion, if they change in such a way that the ratio of the two values of x is the same as the ratio of the corresponding two values of y. The quantity x (which causes the quantity y to change) is called the independent variable, while the quantity y is called the dependent variable.
For your better understanding, we would like to give you some example –
Example.1) If 10 toys cost around $ 95, then find out the cost of 22 toys
Ans.) If 10 toys cost is $ 95 then 22 such toys will cost $ 209
Let, the number of toys = x and the cost of toys = y
10
So, the ratio of the two values of x = -------- and the ratio of
22
95
the corresponding values of y = -------- 209
10 95
Since -------- = --------,
22 209
here the cost of toys varies directly with the number of toys. (Ans.)
Example.2) Christopher have purchased 5 T-shirts cost around $ 750, if he would have purchased 25 T-shirts then what would be the total cost ?
Ans.) As per the given condition, the cost of 5 T-shirts is around $ 750
$ 750
The cost of 1 T-shirt is = ----------- 5
[ here we have divided by given quantity (5 t-shirts) to total cost ($ 750), because the cost of 1 t-shirt will be less than the cost of 5 t-shirts ]
25
The cost of 25 T-shirts will be = $ 750 X --------- 5 = $ 750 X 5 = $ 3750
[ here we have multiplied the given quantity (25 T-shirts) with the cost of 1 T-shirt, because here logically cost of 25 T-shirts will be high than cost of 1 T-shirt ]