Step-by-step explanation:

(i) Let the number of boys who took part in the quiz be x, then the number of girls who took part in the quiz is x+4.

The total number of students who took part in the quiz is 10.

So, x+(x+4) = 10

Simplifying, we get 2x+4=10

or 2x=6

or x=3

Therefore, the number of boys who took part in the quiz is 3 and the number of girls who took part in the quiz is 3+4=7.

Hence, the required pair of linear equations is:

x + y = 10 ...(1)

x - y = -4 ...(2)

(ii) Let the cost of one pencil be x and the cost of one pen be y.

According to the given statement, we have:

5x + 7y = 50 ...(1)

7x + 5y = 46 ...(2)

Hence, the required pair of linear equations is:

5x + 7y = 50 ...(1)

7x + 5y = 46 ...(2)

Verified answer

Answer:

(i) Total number of students who took part in the the quiz =10

Let, the number of boys who took part in the quiz =x

and, number of girls who took part in the quiz =y

According to question,

x+y=10           ...........(1)

y=x+4            ..........(2)

By putting value of x=10−y in equation(2), we get

y=10−y+4

or, 2y=14

So, y=

2

14

=7

and x=10−7=3

Therefore,

Number of  boys who took part in the quiz =3

Number of girls who took part in the class =7

(ii) Let the cost of a pencil be x and cost of one pen be y.

⇒5x+7y=50.......(1)

⇒7x+5y=46.......(2)

Adding and subtracting (1) and (2)

⇒2x−2y=−4

⇒12x+12y=96

⇒x−y=−2.........(3)

⇒x+y=8...........(4)

Add (3) and (4)

⇒2x=6

⇒x=3

⇒3−y=−2

⇒y=5

cost of one pencil=Rs 3

cost of one pen=Rs 5

Step-by-step explanation:

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