Question

18pens and 32pencils together cost 642 , while 32pens and 18pencils together cost 908, find cost of each pen and that of each pencil?
rupees!take

Answer 1

Given

• 18 pens + 32 pencils = ₹ 642
• 32 pens + 18 pencils = ₹ 908

To find

• Cost of 1 pen
• Cost of 1 pencil

Solution

☯ Let cost of each pen be ₹ x and each pencil ₹ y

• 18x + 32y = 642 - (i)
• 32x + 18y = 908 - (ii)

☯ Add (i) and (ii)

• 50x + 50y = 1550
• 50 (x + y) = 1550
• (x + y) = ¹⁵⁵⁰⁄₅₀
• (x + y) = 31 - (iii)

☯ Subtract (i) from (ii)

• 14x - 14y = 266
• 14(x - y) = 266
• (x - y) = ²⁶⁶⁄₁₄        (Substitution method)
• (x - y) = 19

☯ Add (iii) and (iv)

• 2x = 50
• x = ⁵⁰⁄₂
• x = 25

☯ Subtract (iv) from (iii)

• 2y = 12
• y = ¹²⁄₂
• y = 6

☯️ ∴ Cost of each pen (x) = ₹ 25

☯️ ∴ Cost of each pencil (y) = ₹ 6

Verification

☯ Substitute x and y in (iii)

• x + y = 31
• 25 + 6 = 31
• 31 = 31
• L.H.S = R.H.S

Answer 2

Answer:

let pens be x and pencils be y

from first condition,

18x + 32y = 642

Divide equation by 2

•°• 9x + 16y = 321___(1)

from second condition,

32x + 18y = 908

Divide equation by 2

•°• 16x + 9y = 454___(2)

1.) Addition of equation (1) & (2)

9x + 16y = 321

+

16x + 9y = 454

_______________

25x + 25y = 775

Divide equation by 25

•°• x + y = 31___(3)

2.) Subtraction of equation (2) from (1)

9x + 16y = 321

–

16x + 9y = 454

_______________

–7x + 7y = –133

Divide equation by 7

•°• –x + y = –19___(4)

3.) Addition of equation (3) & (4)

x + y = 31

+

–x + y = –19

_______________

2y = 12

y = 12/2

y = 6

4.) Substituting the value of y in equation (3)

x + y = 31

x + 6 = 31

x = 31 - 6

x = 25

The cost of one pen = x = ₹25

The cost of one pencil = y = ₹6