Name: What is an Equation?
Uploaded: 2019-07-19
Duration: 3 min 1 s
Description: If I have ten oranges and you have x number of oranges which add up to 30 oranges, then we have an equation ready, which is 10 + x = 30. It is that simple! L...

Question

Raju bought seven notebooks of two hundred pages and five of hundred pages, for

107

rupees. Joseph bought five notebooks of two hundred pages and seven of hundred pages, for

97

rupees. What is the price of each kind of notebook?

Accepted Answer

Let the price of each notebook two hundred pages be $₹ x$ and that of each notebook of one hundred pages be $₹ y$

So, by the given condition we get, $₹ 7 x + ₹ 5 y = 107 \Rightarrow 7 x + 5 y = 107$ ----(i)

and, $₹ 5 x + ₹ 7 y = ₹ 97 \Rightarrow 5 x + 7 y = 97$ -----(ii)

Subtracting (ii) from (i), we get, $(7 x + 5 y) - (5 x + 7 y) = 107 - 97$

$\Rightarrow 7 x + 5 y - 5 x - 7 y = 10$

$\Rightarrow 2 x - 2 y = 10$

$\Rightarrow 2 (x - y) = 10$

$\Rightarrow x - y = \frac{10}{2} = 5$

$\Rightarrow x = 5 + y$ -----(iii)

Putting the value of $x$ from (iii) in (i), we get, $7 x + 5 y = 107$

$\Rightarrow 7 (5 + y) + 5 y = 107$

$\Rightarrow 35 + 7 y + 5 y = 107$

$\Rightarrow 12 y = 107 - 35$

$\Rightarrow 12 y = 72$

$\Rightarrow y = \frac{72}{12} = 6$

$\Rightarrow y = 6$

Putting the value of $y = 6$ in (iii), we get, $x = 5 + y$

$\Rightarrow x = 5 + 6$

$\Rightarrow x = 11$

Therefore, the price of each two hundred pages notebook is $₹ 11$ and that of each one hundred pages notebook is $₹ 6$ .

Kerala Board Solutions for Chapter: Pairs of Equations, Exercise 2: Exercise 2

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Pairs of Equations, Exercise 2: Exercise 2

Questions from Kerala Board Solutions for Chapter: Pairs of Equations, Exercise 2: Exercise 2 with Hints & Solutions

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