Question

5 pens, 8 notebooks and 3 pencils cost Rs.132; 3 pens, 4 notebooks and 2 pencils cost Rs.74; 6 pens, 3 notebooks and 4 pencils cost Rs.108. Find the cost totally of 2 pens, 4 pencils and 3 notebooks.​

Answer 1

314 is the answer ohh yeah

Answer 2

Step-by-step explanation:

Step 1.

Let the cost of 1 pen be x, 1 notebook be y and 1 pencil be z.

Step 2.

5 pens, 8 notebooks and 3 pencils cost Rs. 132

⇒ 5x + 8y + 3z = 132 ... ... (i)

3 pens, 4 notebooks and 2 pencils cost Rs. 74

⇒ 3x + 4y + 2z = 74 ... ... (ii)

6 pens, 3 notebooks and 4 pencils cost Rs. 108

⇒ 6x + 3y + 4z = 108 ... ... (iii)

Step 3.

Now, (i) × 3 - (ii) × 5 ⇒

15x + 24y + 9z - 15x - 20y - 10z = 386 - 370

⇒ 4y - z = 16 ... ... (iv)

Again, (ii) × 2 - (iii) × 1 ⇒

6x + 8y + 4z - 6x - 3y - 4z = 148 - 108

⇒ 5y = 40

⇒ y = 8

Step 4.

Putting y = 8 in (iv), we get

4 (8) - z = 16

⇒ 32 - z = 16

⇒ z = 32 - 16

⇒ z = 16

Step 5.

Putting y = 8 and z = 16 in (i), we get

5x + 8 (8) + 3 (16) = 132

⇒ 5x + 64 + 48 = 132

⇒ 5x + 112 = 132

⇒ 5x = 132 - 112

⇒ 5x = 20

⇒ x = 4

Then the cost of 1 pen is Rs. 4, 1 notebook is Rs. 8 and 1 pencil is Rs. 16.

Step 6.

Therefore the total cost of 2 pens, 4 pencils and 3 notebooks

= Rs. 2 (4) + 4 (16) + 3 (8)

= Rs. 8 + 64 + 24

= Rs. 176

Final answer:

The total cost of 2 pens, 4 pencils and 3 notebooks is Rs. 176.