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.
