Question

2. The cost of 8 books and 5 pens is 420 rupees and the total cost of 5 books
and 8 pens is 321 rupees. Find the cost of a book and a pen.​

Answer 1

LET THE COST OF A BOOK & PEN BE x AND y.

A/q,

8x+5y = 420 ----(i)

5x+8y = 321 ----(ii)

(i)×5 = 5(8x+5y = 420)

= 40x+25y=2100 ----(iii)

(ii)×8 = 8( 5x+8y = 321)

= 40x+64y = 2568 ----(iv)

Subtracting eq. (iv) from (iii)

40x+64y = 2568

40x+25y= 2100

(-) (-) (-)

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

39y = 468

=> y= 468/39

=> y= 12

Now , Put the value of y = 12 in eq. (i)

8x+5y = 420

8x+5(12) = 420

8x+60 = 420

8x = 420-60

8x = 360

x=360/8

x= 45

THEREFORE, THE COST OF A BOOK IS ₹45 & THE COST OF A PEN IS ₹12.

Answer 2

Given:

• The cost of 8 books and 5 pens is 420 rupees.
• The total cost of 5 books and 8 pens is 321 rupees.

To find:

• The cost of a book and a pen.?

Solution:

• Let's consider cost of book be x & cost of pen be y.

Where,

• 8x + 5y = 420
• 5x + 8y = 321

• Let 8x + 5y = 420 be Equation 1... & 5x + 8y = 321 be Equation 2...

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, let's find y first,

→ 5(8x + 5y = 420)

• Multiplying it by 5 because there are 5 pens.

→ 40x + 25y = 2100

• Let 40x + 25y = 2100 be equation (iii)...

→ 8(5x + 8y = 321)

• Multiplying it by 8 because there are 8 pens.

→ 40x + 64y = 2568

• Let 40x + 64y = 2568 be equation (iv)...

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, let's Subtract equation (iii) from (iv),

→ 40x + 64y = 2568 - 40x + 25y = 2100

→ 40x - 40x + 64y + 25y = 2568 - 2100

→ 0 + 39y = 468

→ y = 468/39

→ y = 12

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Let's Find x by putting the values of y in equation 1...,

As we know that,

8x + 5y = 420

→ 8x + 5(12) = 420

→ 8x + 60 = 420

→ 8x = 420 - 60

→ 8x = 360

→ x = 360/8

→ x = 45

∴ Hence, Cost of book is 45 rupees & cost of pen is 12 rupees.