Question

d) The price of 2 notebooks and 3 textbooks is 120, but a notebook costs 10 more than the
textbook. Find the cost of both; the notebook and text book.
​

Answer 1

Given :

• Price of 2 notebooks and 3 textbooks is 120.
• But a notebook costs 10 more than the textbook.

To find :

• The cost of notebook and textbook.

According to the question,

• Let the cost of textbook be x
• And the cost of notebook be (x + 10)

➙ 2 notebook + 3 textbook = 120

➙ 2(x + 10) + 3(x) = 120

➙ 2x + 20 + 3x = 120

➙ 5x + 20 = 120

➙ 5x = 120 - 20

➙ 5x = 100

➙ x = 100 ÷ 5

.°. x = 20

So,the cost of textbook is 20

And the cost of notebook is (x + 10) = (20 + 10) = 30

Answer 2

Let the cost of textbook be "y" and notebook be "x".

Given that:

⇒ 2x + 3y = 120......[1]

⇒ y + 10 = x

Since, they are forming simultaneous equations, therefore we can solve them.

Here, we can use elimination method to solve them.

First converting y + 10 = x into its standard form

y + 10 = x

y - x = -10

x - y = 10.....[2]

Solving [1] and [2] by elimination.

Eliminating x,

Multiplying [2] by 2 will give,

2(x - y = 10) = 2x - 2y = 20

2x + 3y = 120.....[1]

2x - 2y = 20.....[2]

Subtracting [2] from [1]

2x + 3y = 120

-(2x - 2y = 20)

______________

5y = 100

y = $\sf \cancel{\dfrac{100}{5}}=20$

$\bigstar\boxed{ \bf y = 20}\bigstar$

Substituting the value of y in [2]

→ x - y = 10

→ x - 20 = 10

→ x = 20 + 10

→ x = 30

$\bigstar\boxed{ \bf x = 30}\bigstar$

Therefore, the cost of notebook is 30 and cost of textbook is 20.