Question

1. Form the pair of linear equations in the following problems, and find their solutions graphically.

(1) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in
the quiz.

(ii) 5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of one pencil and that of one pen.​

Answer 1

☆ Answer ☆

★ Given :-

• 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys.

★ Have to Find :-

• Find the number of boys and girls who took part in the quiz.

★ Solution :-

$\red{\bigstar}$ Number of Boys

$\large\leadsto\boxed{\sf\purple{3}}$

$\red{\bigstar}$ Number of girls

$\large\leadsto\boxed{\sf\purple{7}}$

Step by Step Explanation

Let's consider the number of boys be " x "

As according to the Question

Number of girls is 4 more than the number of boys

So,

No. of Girls = x + 4

Number of students participated in quiz = 10

Now,

Number of boys + Number of girls = 10

➹ x + x + 4 = 10

➹ 2x + 4 = 10

➹ 2x = 10 - 4

➹ 2x = 6

➹ x = 6 / 2

$\longmapsto\tt{x=\cancel\dfrac{6}{2}}$

➹ x = 3

Hence,

• Number of boys = x

= 3

• Number of girls = x + 4

=3 + 4

= 7

________________________

★ Given :-

• 5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46.

★ Have to Find :-

Find the cost of one pencil and that of one pen.

★ Solution :-

$\red{\bigstar}$ Cost of 1 pencil

$\large\leadsto\boxed{\sf\purple{Rs. \: 3}}$

$\red{\bigstar}$ Cost of 1 pen

$\large\leadsto\boxed{\sf\purple{Rs. \: 5}}$

Step by Step Explanation

Let's we consider the cost of one pencil be "x" and the cost of one pen be "y."

As per the Question

Cost of pen + Cost of Pencil = 5x + 7y = 50 .....( 1 )

Or

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

Multiplying ( 1 ) eqn with 7, we get,

= 35x + 49y = 350 .....( 3 )eqn

Multiplying ( 2 ) eqn with 5, we get,

= 35x + 25y = 230 .....( 4 )eqn

Now, Subtracting ( 4 )eqn from ( 3 )eqn ,

➹ 24y = 120

➹ y = 120/24

$\longmapsto\tt{x=\cancel\dfrac{120}{24}}$

➹ y = 5

Then, putting value of y in equation ( 1 ) ,

➹ 5x + 7 × 5 = 50

➹ 5x = 15

➹ x = 15/5

$\longmapsto\tt{x=\cancel\dfrac{15}{3}}$

➹ x = 3

Hence ,

• Cost of one pencil = x

= Rs. 3

• Cost of one pen = y

= Rs. 5

________________________

Answer 2

Answer:

(1) 10 students of Class X took part in a Mathematics quiz.

x + y = 10

If the number of girls is 4 more than the number of boys,

Number of girls = number of boys + 4

x = y + 4

x - y = 4

And

x + y = 10

Solving the equation

2x = 14

x = 7

y = 5

So the number of boys is 5 and girls is 7 who took part in the quiz.

(ii) 5 pencils and 7 pens together cost ₹50,

$5x + 7y = 50$

whereas 7 pencils and 5 pens together cost ₹46.

$7x + 5y = 46$

5x+7y=50 and

7x+5y=46 for the variables x and y.

The solutions to your equations are:

x= 3 and y= 5

So the cost of one pencil ✏ is 3 and that of one pen is 5.