Question

Raju bought 7 notebooks of two hundred pages and 5 notebooks 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 note book?​

Answer 1

$[tex] \large \dag$ Question :-

Raju bought 7 notebooks of two hundred pages and 5 notebooks 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 note book?

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{Cost   \: of \:  200  \: pages \:  notebook = Rs\: 11}} }$

$\red\dashrightarrow\underline{\underline{\sf  \green{Cost   \: of \:  100  \: pages \:  notebook = Rs\: 6}} }$

$\large \dag$ Step by step Explanation :-

Let us Assume that,

Cost of Notebook with Two Hundred pages be = Rs $\large\rm x$

Cost of Notebook with Hundred pages be= Rs $\large \rm y$

❒ As Raju bought 7 notebooks of 200 pages and 5 notebooks of 100 pages for Rs 107 :-

$\rm\large\green \dashrightarrow\blue{ \underline{ \underline{7x + 5y = 107}}}$

$:\longmapsto \rm 5y = 107 - 7x$

$\orange{ \large :\longmapsto  \underline {\boxed{{\bf y = \frac{107 - 7x}{5} } }}}- - - (1)$

❒ As Joseph bought 5 notebooks of 200 pages and 7 of 100 pages for Rs 97 :-

$\rm\large\green \dashrightarrow\blue{ \underline{ \underline{5x + 7y = 97}}} - - - (2)$

⏩ Substituting (1) in (2) ;

$:\longmapsto \rm 5x + 7 \bigg( \frac{107 - 7x}{5} \bigg) = 97$

$:\longmapsto \rm 5x + \frac{749 - 49x}{5} = 97$

$:\longmapsto \rm \frac{25x + 749 - 49x}{5} = 97$

$:\longmapsto \rm {749 - 24x} = 485$

$:\longmapsto \rm - 24x = 485 - 749$

$:\longmapsto \rm \cancel- 24x = \cancel - 264$

$:\longmapsto \rm y = \cancel \frac{264}{24}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 11} }}}$

Therefore,

$\underline{\pink{\underline{\frak{\pmb{\text Cost   \: of \:  200  \: pages \:  notebook = Rs\: 11}} }}}$

⇝ Putting Value of x in (1) ;

$:\longmapsto \rm y = \frac{107 - 7 \times 11}{5}$

$:\longmapsto \rm y = \frac{107 - 77}{5}$

$:\longmapsto \rm y = \cancel \frac{30}{5}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf y = 6} }}}$

Therefore,

$\underline{\pink{\underline{\frak{\pmb{\text Cost   \: of \:  100  \: pages \:  notebook = Rs\: 6}} }}}$[/tex]

Answer 2

Answer:

Let the price of two hundred pages notebook be ‘x’ and price of hundred pages book be ‘y’.

According to the question,

Raju bought 7 notebooks of two hundred pages and five of hundred pages for 107 rupees

⇒ 7x + 5y = 107 ... (1)

Joseph bought five notebooks of two hundred pages and seven of hundred pages, for 97 rupees

⇒ 5x + 7y = 97… (2)

Equating (1) and (2)

7x + 5y = 107

5x + 7y = 97

Multiply Equation (1) by 7 and equation (2) by 5

Multiply Equation (1) by 7 and equation (2) by 5Then, Subtract equation (2) from (1)

49x + 35y = 749

-25x - 35y = -485

24x = 264

x = 264/24

x = 11

Put x = 11 in Equation (3)

49 × 11 + 35 y = 749

⇒ 539 + 35y = 749

⇒ 35y = 749 – 539

⇒ 35y = 210

⇒ y = 210/35

⇒ y = 6

Hence, price of two hundred pages notebook is 11rupees and price of hundred pages notebook is 6 rupees.

Step-by-step explanation:

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