Question

the price of three pencils and five pens is 34 rupees.And for 5 pencils and 6 pens it is 45 rupees. what is the price of each? explain​

Answer 1

Answer:

let pencils be x

let pens be y

the price of 3 pencils and 5 pens is 34

3x+5y=34--------(1)

the price of 5pencils and 6 pens is 45

5x+6y=45--------(2)

now do (1)*5and (2)*3

so,

15x+25y=170------(3) &

15x+18y=135-------(4) (doing 3-4)

- - -

--------------------

0+7y=35

y=35/7

y=5

now substitute y=5 in (1)

3x+5(5)=34

3x=34-25

3x=9

x=3.

now, the cost of one pencil (x) =3

the cost of one pen (y)=5.

this is the answer

Answer 2

Given :

The price of three pencils and five pens is 34 rupees. And for 5 pencils and 6 pens it is 45 rupees.

To Find :

• What is the price of each pen and pencil?

Solution :

Let,

• The price of a pen be x.
• The price of a pencil be y.

From the question, we get two equations :

⟼ 3y + 5x = 34ㅤㅤㅤ⟮Equation No. 1⟯

⟼ 5y + 6x = 45ㅤㅤㅤ⟮Equation No. 2⟯

From equation no. 2, we get :

⇢ 5y + 6x = 45

⇢ 5y = 45 - 6x

⇢ y = 45 - 6x/5

Substituting the value of y in equation no. 1, we get :

⇢ 3y + 5x = 34

⇢ 3(45 - 6x)/5 + 5x = 34

⇢ (135 - 18x)/5+ 5x = 34

⇢ (135 - 18x + 25x)/5 = 34

⇢ (135 + 7x)/5 = 34

⇢ 135 + 7x = 34 × 5

⇢ 7x = 170 - 135

⇢ x = 35/7

⇢ x = 5

Substituting the value of x in equation no. 2, we get :

⇢ 5y + 6x = 45

⇢ 5y + 6(5) = 45

⇢ 5y + 30 = 45

⇢ 5y = 45 - 30

⇢ y = 15/5

⇢ y = 3

∴ The cost of each pen and pencil is Rs. 5 and Rs. 3 respectively.