An equation is a statement that two numbers or expressions are equal.
An Equation has two equal parts. Equations are useful for relating
variables and numbers. Many word problems can easily be written down as
equations with a little practice.
e.g., 5x + 2 = 12
When an equation has a variable, the solution to the equation is the
number that makes the equation true when we replace the variable with its
value. This also called as the root of the equation.
We say x = 2 is a solution to the equation 4x + 5 = 13, for replacing
each occurrence of x with 2 gives us 4 × 2 + 5 = 13 ==> 8 + 5 = 13
==> 13 = 13 which is true.
Simple Equation: Degree of an equation is the highest
power of the variable used. If an equation has only one parameter with
degree 1 then it is called as simple equation. Simple equations have only
one variable of degree one. Hence when simplified it gives only one value
as its root.
Simultaneous equations: If an equation of degree 1 has
two or more than two variables then we cannot solve it to get unique value
as its roots.
Averages
Arithmetic mean and Geometric mean are measures of central tendency.
The other forms are mode and median, which we will be covering in
statistics.
Arithmetic mean
The Average or Mean or Arithmetic Mean of a group of quantities of the
same kind is their sum divided by the numbers of quantities.
Example
1. A woman is five years younger than her husband and three times
as old as her daughter. If the daughter attains the age of 21 after six
years, what is the present age of the father?
(A) 45 years
(B) 50 years
(C) 55 years
(D) 40 years
(E) 60
years
Solution: Husband’s age = x years. Therefore, Woman's age = x
– 5 years.
Therefore Daughter's age =  , Therefore -- + 6 = 21
i.e. x = 50.
Hence (B)
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