Question

The total cost of 8 books and 6 pens is 150 and the total cost of 10 books and 4 pens is 170. Find the cost of 1 book 2 pens.​

Answer 1

Answer:

Cost of 1 book and 2 pens is 25.

Step-by-step explanation:

Given :

• The total cost of 8 books and 6 pens is 150.
• The total cost of 10 books and 4 pens is 170.

To find :

the cost of 1 book and 2 pens.​

Solution :

Let the cost of 1 book be x and the cost of 1 pen be y.

➙ Cost of 8 books = 8x

➙ Cost of 6 pens = 6y

The total cost of 8 books and 6 pens is 150

8x + 6y = 150 ➙ [1]

➙ Cost of 10 books = 10x

➙ Cost of 4 books = 4y

The total cost of 10 books and 4 pens is 170.

 10x + 4y = 170

 2(5x + 2y) = 2(85)

 5x + 2y = 85 ➙ [2]

Multiplying the equation [2] by 3, we get

15x + 6y = 255 ➙ [3]

Subtract equation [1] from equation [3],

15x + 6y - (8x + 6y) = 255 - 150

15x + 6y - 8x - 6y = 105

 7x = 105

  x = 105/7

  x = 15

∴ Cost of 1 book is 15

Substitute x = 15 in equation [1],

8(15) + 6y = 150

120 + 6y = 150

  6y = 150 - 120

  6y = 30

   y = 30/6

   y = 5

∴ Cost of 1 pen is 5

➙ Cost of 1 book and 2 pens = x + 2y

➙ 15 + 2(5)

➙ 15 + 10

➙ 25

∴ Cost of 1 book and 2 pens is 25