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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