We will learn ‘what direct variation is’ and how to solve different types of problems on some situations of direct variation.
If two quantities are related in such a way that the increase in one quantity results in a corresponding increase in the other and vice versa, then such a variation is called a direct variation.
If the two quantities are in direct variation then we also say that they are proportional to each other.
Suppose, if the two quantities ‘x’ and ‘y’ are in direct variation, then the ratio of any two values of x is equal to the ratio of the corresponding values of y.
i.e., \(\frac{x_{1}}{x_{2}} = \frac{y_{1}}{y_{2}}\)
or, \(\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}}\)
Some situations of direct variation:
● More articles, more money required to purchase
Less articles, less money required to purchase.
● More men at work, more work is done..
Less men at work, less work is done.
● More money borrowed, more interest is to be paid.
Less money borrowed, less interest to be paid.
● More speed, more distance covered in fixed time.
Less speed, less distance covered in fixed time.
● More working hours, more work will be done.
Less working hours, less work will be done.
Problems on different
situations of direct variation:
1. If 12 flowerpots cost $156, what do 28 flowerpots cost?
Solution:
This is the situation of direct variation as
More flowerpots, result in more cost.
Cost of 12 flowerpots = $ 156
Cost of 1 flowerpot = $ (156/12)
Cost of 28 flowerpots = $ (156/12 × 28) = $ 364
2. A motor bike travels 280 km in 40 liters of petrol. How much distance will it cover in 9 liters of petrol?
Solution:
This is the situation of direct variation.
Less quantity of petrol, less distance covered.
In 40 liters of petrol, distance covered = 280 km
In 1 liter of petrol, distance covered = 280/40 km
In 9 liters of petrol, distance covered = 280/40 × 9 km = 63 km
Situations of Direct Variation
Situations of Inverse Variation
Direct Variations Using Unitary Method
Direct Variations Using Method of Proportion
Inverse Variation Using Unitary Method
Inverse Variation Using Method of Proportion
Problems on Unitary Method using Direct Variation
Problems on Unitary Method Using Inverse Variation
Mixed Problems Using Unitary Method
7th Grade Math Problems
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