Algebra (Exercise 11.1)

Algebra


Exercise 11.1


EX 11.1 QUESTION 1.


Find the rule which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.

(a) A pattern of letter T as T
(b) A pattern of letter Z as Z
(c) A pattern of letter U as U
(d) A pattern of letter V as V
(e) A pattern of letter E as E
(f) A pattern of letter S as S
(g) A pattern of letter A as A

Solution:

(a) A pattern of letter T = 2n ( as two matchsticks are required to make a letter T)

(b) A pattern of letter Z = 3n ( as three matchsticks are required to make a letter Z)

(c) A pattern of letter U = 3n  ( as three matchsticks are required to make a letter U)

(d) A pattern of letter V = 2n  ( as two matchsticks are required to make a letter V)

(e) A pattern of letter E  = 5n  ( as five matchsticks are required to make a letter E)

(f) A pattern of letter S  = 5n  ( as five matchsticks are required to make a letter S)

(g) A pattern of letter A = 6n  ( as six matchsticks are required to make a letter A)


EX 11.1 QUESTION 2.


We already know the rule for the pattern of letters L, C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?

Solution:

The letter Z and U have a pattern 3n, therefore 3 matchsticks required to make the letter Z and U.


EX 11.1 QUESTION 3.


Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows)

Solution:

Number of rows = n

Number of cadets in each row = 5

Total number of cadets =  number of rows × number of cadets in a row

= 5 × n

= 5n


EX 11.1 QUESTION 4.


 If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)

Solution:

Number of boxes = b

Number of mangoes in each box = 50

Total number of mangoes = number of boxes× number of mangoes in a box

= 50 × b

= 50b


EX 11.1 QUESTION 5.


The teacher distributes 5 pencils per students. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)

Solutions:

Number of students = s

Number of pencils are given to each student = 5

Total number of pencils = number of pencils given to each student × number of students

= 5s


EX 11.1 QUESTION 6.


A bird flies 1 kilometer in one minute. Can you express the distance covered by the birds in terms of its flying time in minutes? (Use t for flying time in minutes.)

Solutions:

Flying times taken by bird = t minutes

Distance covered by a bird in one minute = 1 km

Distance covered in t minutes = Distance covered in one minute × Flying time

= 1 × t

= t km


EX 11.1 QUESTION 7.


Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?

Solutions:

Number of dots in a row = 9

Number of rows = r

Total number of dots in r rows = Number of dots in a row × number of rows

= 9r

Number of dots in 8 rows = 8 × 9

= 72

Number of dots in 10 rows = 10 × 9

= 90


EX 11.1 QUESTION 8.


Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Can you write Leela’s age in terms of Radha’s age? Take Radha’s age to be x years.

Solutions:

Let Radha’s age be = x years

Leela’s age = 4 years younger than Radha

= (x – 4) years


EX 11.1 QUESTION 9.


Mother has made laddus. She gives some laddus to guests and family members; still 5 laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?

Solutions:

Number of laddus mother gave = l

Remaining laddus = 5

Total number of laddus = number of laddus given away by mother + number of laddus remaining

= (l + 5) laddus


EX 11.1 QUESTION 10.


Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be x, what is the number of oranges in the larger box?

Solutions:

Number of oranges in a small box = x

Number of boxes = 2

Therefore the number of oranges in two small boxes = 2x

Remaining oranges = 10

Number of oranges in large box = number of oranges in two small boxes + number of oranges remained

= 2x + 10


EX 11.1 QUESTION 11.


(a) Look at the following matchstick pattern of square. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares.
(Hint: If you remove the vertical stick at the end, you will get a pattern of Cs)

Solution:
(a) Let the number of squares = n

∴ Number of matchsticks required

For n = 1

3 x n + l = 3n + 1 = 4

For n = 2

3 x n + l = 3n + 1 = 7

For n = 3

3 x n + l = 3n + 1 = 10

For n = 4

3 x n + l = 3n + 1 = 13

∴ Rule is 3n + 1 where n represents the number of squares.

(b) Let the number of triangles = n

∴ Number of matchsticks required

For n = 1

2n + 1 = 3

For n = 2

2n + 1 = 5

For n = 3

2n + 1 = 7
For n = 4

2n + 1 = 9

∴ Rule is 2n + 1 where n represents the number of matchsticks.