Can you explain what is direct and indirect variations and how to solve it​

(150x3)20
450x20
ans. 9000

Direct variation is a relationship between two variables where one is dependent on the other and where a common factor or constant is present.  

When two variables vary directly, it means that when the independent variable increases, the dependent variable also increases.  When the independent variable decreases, the dependent variable also decreases.

The key words are:
* directly varies or varies directly
*varies proportionately 
* is directly proportionate

If these phrases are present in the problem, then the direct variation equation is in the form:

y = kx   or   any letter to represent y and x with k as constant of the variation.

Where x is the independent variable and y is the dependent variable.

Some examples of direct variation formula in real life:

Circumference of a Circle = 2πr   where r (radius) is the independent variable
                                                        and 2π is the direct variation constant.

f(L) = 45L    Where f(L) is the total cost of fuel,  and 45 is constant 
                     representing fuel price per liter, and L is the volume of fuel
                     (gas/diesel) bought. 
     
It is important to know not just the direct variation for y = kx because it is expressed in many forms in real life situation.

Example:

If the circumference of a circular garden is to be enlarged twice the original circumference, what should be the radius of the bigger garden if the original radius is 5 ft?

Solution:

C = 2πr

Original garden:
radius = 5 ft

The circumference of the original garden:

C = 2π(5 ft)
   = 10π  ft  or  31.4 ft.

What is the radius of the enlarged garden when the circumference is twice the original?

2 (31.4 t) = 2πr

62.8 ft = 2πr

r = 62.8 ft/6.28

r = 10 ft.

Interpretation according to the definition of direct variation:

When the radius (the independent variable) is doubled, the circumference (the dependent variable) is also doubled.

This is how the relationship of the variables C (circumference) and r (radius) is described in direct variation.

I hope that you realize that it's not just  y=kx. If you know the key phrases and the definition (and the relationship), you can solve real-life situation problem involving direct variation.

The equation of this variation is written in a form of: y = kx

k represents as a constant:

If the variable y is bigger than variable x, the constant will increase.

If the variable y is smaller than variable x, the constant will decrease.

Example:

equation: y = kx

y = 6 and x = 3

(6) = k(3)

6/3 = 3k/3

2 = k

Another example:

equation: y = kx

y = 4 and x = 12

(4) = k(12)

4/12 = 12k/12

⅓ = k