More Examples of Variables
When trying to denote a variable, any alphabet can be used.
Note that, a variable is a number representation which does not have a
Example for fixed values:
The number 5 or the number 100 or any other given number is not a variable. They have fixed values.
Similarly, the number of angles of a triangle has a fixed value i.e.
The number of corners of a quadrilateral i.e.
But n in the examples we have looked is a variable.It takes on various values 1, 2, 3, 4, ... .
Now see this problem: A bunch of students went to buy notebooks from the school bookstore. Price of one notebook is Rs. 5. Sarita wants to buy 5 notebooks, Rahul wants to buy 7 notebooks, Rehman wants to buy 4 notebooks and so on. How much money should a student carry when she or he goes to the bookstore to buy notebooks?
It is obvious that the value will depend on how many notebooks the respective student wants to buy. The students work together to prepare a similar table as earlier.
| Number of Notebooks | Total cost of notebooks |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | |
| 5 | |
| m | |
| ... | ... |
The letter m stands for the number of notebooks a student wants to buy, where m is a variable. The total cost of m notebooks is given by the rule :
The total cost in rupees = 5 × number of note books required= 5m
If Sarita wants to buy 5 notebooks, then she should carry Rs.
Let's work with another example. During the Republic Day celebration, children are supposed to perform a mass drill in the presence of the chief guest. They stand 10 in a row. How many children can there be in the drill?
The number of children will depend on the number of rows.
If there is 1 row, there will be 10 children. If there are 2 rows, there will be 2 × 10 or 20 children and so on. If there are r rows, there will be
Here,r is a variable which stands for the number of rows and so takes on values 1, 2, 3, 4 and so on.
In all the examples seen so far, the variable was multiplied by a number. However, it is not always the same and different situations arise where numbers are added to or subtracted from the variable as well. Let's see how.
Sarita says that she has 10 more marbles in her collection than Raju. If Raju has 20 marbles, then Sarita has
If Raju has 30 marbles, then Sarita has
Since, we do not know exactly how many marbles Raju has, we can represent that number with a
Sarita's marbles = Raju's marbles +
Let's say, Raju's marbles are represented by the variable x.
Then, Sarita's marbles are represented by
Here, x is a variable which stands for the number of marbles Raju has.
The expression x + 10 is read as x plus ten. It means 10 added to x.
If x is 20, x + 10 is 30. If x is 30, x + 10 is 40 and so on.
Is x + 10 different from 10x ?
Yes, they are different.How to interpret them?
" x + 10 " means that x is getting
Another example: Raju and Rahul are brothers. Rahul is younger than Raju by 2 years. When Raju is 12 years old, Rahul is 10 years old. When Raju is 15 years old, Rahul is
We, again, do not know Raju’s age exactly. It may have any value. Let x denote Raju’s age in years, x is a variable. If Raju’s age in years is x, then Rahul’s age in years is
The expression (x – 2) is read as x minus two. As you would expect, when x is 12, (x – 2) is