Page 213 - Start Up Mathematics_6

Example 1: Find the rule which gives the number of matchsticks required to make the pattern
by putting the following letters next to one another in a sequence. Use a variable to
write the rule.

(a) A pattern of letter S as (b) A pattern of letter A as

Solution: (a) The rule for pattern of letter S is given in the following table:

, , , , ... .

Number of letters ‘S’ 1 2 3 4 5 … n
Number of matchsticks 5 10 15 20 25 … 5n
(b) The rule for pattern of letter A is given in the following table:

, , , , ... .

Number of letters ‘A’ 1 2 3 4 5 … n
Number of matchsticks 6 10 14 18 22 … 4n + 2

Example 2: If there are 60 apples in a box, how will you write the total
number of apples in terms of the number of boxes?
Solution: Number of apples in each box = 60
Let the number of boxes be n.

Therefore, total number of apples = 60 × n = 60n
Example 3: On her birthday, Nivedita distributed 4 toffees to each student of her class. Find out
how many toffees are needed if there are 30 students in her class? Can you generalize
the result? (Use k for the number of students.)
Solution: Toffees distributed to each student = 4
Therefore, number of toffees required for 30 students = 4 × 30 = 120

Generalizing the number of toffees required for k students = 4 × k = 4k
Example 4: An eagle flies 500 m in one minute. Can you express the distance in km covered by
the eagle in terms of its flying time in minutes?
1
Solution: Distance covered by the eagle in 1 minute = 500 m = 2 km
Let the bird fly for t minutes.
1 t
Therefore, distance covered in t minutes = t × 2 = 2 km

Example 5: Sita is Radha’s younger sister. Sita is 7 years younger to Radha. Can you write
Radha’s age in terms of Sita’s age?

205