Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 7 Algebra Ex 7.1 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 6 Maths Chapter 7 Algebra Ex 7.1

1. Find the rule which gives the number of matchsticks required to make the following ‘it’ matchstick patterns. Use a variables to write the rule:

Question (i)

A pattern of letter T as

Solution:

Number of matchsticks required in a pattern of letter T = 2

Number of matchsticks required in ‘n’ patterns = 2n

Question (ii)

A pattern of letter E as

Solution:

Number of matchsticks required in a pattern of letter E = 4

Number of matchsticks required in V patterns of letter E = 4n

Question (iii)

A pattern of letter F as

Solution

Number of matchsticks required in a pattern of letter F = 3

Number of matchsticks required in ‘n’ patterns of letter F = 3 n

Question (iv)

A pattern of letter C as

Solution:

Number of matchsticks required in a pattern of letter C = 3

Number of matchsticks required in ‘n’ patterns of letter C = 3n

Question (v)

A pattern of letter S as

Solution:

Number of matchsticks required in a pattern of letter S = 5

Number of matchsticks required in V patterns of letter S = 5 n

2. Students are sitting in rows. There are 12 students in row. What is the rule which gives the number of students in ‘n’ rows? (Represent by table)

Solution:

Let us make a table for the number of students in ‘n’ rows.

Number of Rows | 1 | 2 | 3 | 4 | ….. | 10 | …… | n |

Number of Students | 12 | 24 | 36 | 48 | …… | 120 | …… | 12 n |

It is observed from the table that

Total number of students in ‘n’ number of rows

= (Number of Students) × (Number of rows)

= 12 × n = 12n

3. The teacher distributes 3 pencils to a student What is the rule which gives the number of pencils, if there are ‘a’ number of students?

Solution:

We know

Total number of pencils

= Number of pencils × Number of students

= 3 × a = 3a

4. There are 8 pens in a pen stand. What is the rule that gives the total cost of the pens if the cost of each pen is represented by a variable ‘c’?

Solution:

We know

Total cost of the pens in ₹

= Number of pens × cost of 1 pen

= 8 × c = 8c

5. Gurleen is drawing pictures by joining dots. To make one picture,’she has to join 5 dots. Find the rule that gives the number of dots, if the number of pictures is represented by the symbol ‘p’.

Solution:

We know

Total number of dots = Number of dots × Number of pictures

= 5p

6. The cost of a dozen bananas is ₹ 50. Find the rule of total cost of bananas if there are ‘d’ dozens bananas.

Solution:

We know

Total cost of bananas in ₹

= Cost of one dozen × Number of bananas

= 50 × d

= 50d

7. Look at the following matchsticks patterns of squares given below. The squares are not separate as there are two adjoined adjacent squares have a common match stick. 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 patterns of C)

Solution:

Fig. No. | No. of Squares | Number of matchsticks | Pattern |

(i) | 1 | 4 | 3 x 1+ 1 |

(ii) | 2 | 7 | 3 × 2 + 1 |

(iii) | 3 | 10 | 3 × 3 + 1 |

Thus, we get the rule the number of matchsticks = 3x + 1 or 1 + 3x where x is the number of squares.