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

$\large \dag$ 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,

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

Answer 2

Given : 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?

_______________________________

$\underline{ \frak{Explanation}} :$

$\frak{Let \: us \: assume} \rightarrow \begin{cases} \frak{Cost \: of \: 200 \: pages \: note \: be \: \blue{ a}} \\ \\ \frak{Cost \: of \: 100 \: pages \: note \: book \: be \: \blue{b}} \end{cases}$

$\star \quad \boxed{ \sf{Raju \: Brought}} \\ \\ \green{ \frak{7}} \: \sf notebooks \: of \: \pink{ \frak{200}} \: pages \\ \\ \green{ \frak{5}} \: \sf notebooks \: of \: \pink{ \frak{200}} \: books \\ \\ \rm{Total \: Cost} = \underline{ \frak{107 }} \\ \\ \sf{EQUATION} : \\ \\ \star \quad \boxed{ \boxed{ \frak{ \purple{7a + 5b = 107}}}} \qquad \qquad \lgroup \sf eq(1) \rgroup$

________________________________

$\star \quad \boxed{ \sf{Joseph \: Brought}} \\ \\ \green{ \frak{5}} \: \sf notebooks \: of \: \pink{ \frak{200}} \: pages \\ \\ \green{ \frak{7}} \: \sf notebooks \: of \: \pink{ \frak{100}} \: pages \\ \\ \rm{Total \: Cost} = \underline{ \frak{97}} \\ \\ \sf{EQUATION} : \\ \\ \frak{5a + 7b = 97} \\ \\ \star \quad \boxed{ \boxed{ \frak{ \purple{a = \frac{ 97 - 7b}{5}}}}} \qquad \qquad \lgroup \sf eq(2) \rgroup$

Now, substituting eq(2) in eq(1) we get

$\looparrowright\frak{7a + 5b = 107} \\ \\ \looparrowright\frak{7 (\frac{97 - 7b}{5} )+ 5b = 107} \\ \\ \looparrowright\frak{\frac{679 - 49b}{5}+ 5b = 107} \\ \\ \looparrowright\frak{\frac{679 - 49b}{5}+ \frac{25b}{5} = 107} \\ \\\looparrowright\frak{\frac{679 - 49b + 25b}{5} = 107} \\ \\ \looparrowright\frak{ 679 - 24b= 107(5)} \\ \\ \looparrowright\frak{ 679 - 24b= 535} \\ \\ \looparrowright\frak{ - 24b= 535 - 679} \\ \\ \looparrowright\frak{ - 24b= - 144} \\ \\ \looparrowright\frak{ b= \frac{ - 144}{ - 24} } \\ \\ \looparrowright\frak{ b= \cancel\frac{ - 144}{ - 24}} \\ \\ \star \quad \underline{ \boxed{ \green{ \frak{b = 6}}}}$

Substituting b = 6 in eq (1) we get

$\looparrowright\frak{ 7a + 5b = 107 } \\ \\ \looparrowright\frak{ 7 + 5(6) = 107 } \\ \\ \looparrowright\frak{ 7a + 30 = 107 } \\ \\ \looparrowright\frak{ 7a = 107 - 30 } \\ \\ \looparrowright\frak{ 7a = 77 } \\ \\ \looparrowright\frak{ a = \frac{77}{7} } \\ \\ \looparrowright\frak{ a = \cancel \frac{77}{7} } \\ \\ \star \quad \underline{ \boxed{ \green{ \frak{a = 11}}}}$

$\mathcal{HENCE} \rightarrow \begin{cases} \frak{Cost \: of \: 100 \: pages \: notebook \: is \: \pink{6} } \\ \\ \frak{Cost \: of \: 200 \: pages \: notebook \: is \: \pink{11} } \end{cases}$