Question

the price of 3 pen and 5 book is 65 and the price of 4 pen and 2 book is 40 find the price of each?​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given that price of 3 pen and 5 book is 65
• Price of 4 pen and 2 book is 40

To Find:

• We have to find the price of both times, a pen and a book

Solution:

Let the price of a pen = x

Price of a book = y

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$\underline{\large\mathfrak\red{According \: to \: the \: Question:}}$

Price of 3 pen and 5 book is 65

$\hookrightarrow \sf{3(Price \: of \: Pen) + 5(Price \: of \: Book) = 65}$

$\hookrightarrow \sf{3x + 5y = 65}$ ---------------( 1 )

Price of 4 pen and 2 book is 40

$\hookrightarrow \sf{4(Price \: of \: Pen) + 2(Price \: of \: Book) = 40}$

$\hookrightarrow \sf{4x + 2y = 40}$ -----------------( 2 )

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Multiplying by 2 in equation ( 1 ) and by 5 in equation ( 2 )

• Equation 1 becomes
• $\sf{ 6x + 10y = 130}$ ----------- ( 3 )

• Equation 2 becomes
• $\sf{ 20x + 10y = 200}$ -----------( 4 )

Subtracting Equation ( 3 ) from ( 4 )

$\implies \sf{20x + 10y - 6x - 10y = 200 - 130}$

$\implies \sf{14x = 70}$

$\implies \sf{x = \dfrac{70}{14}}$

$\implies \boxed{\sf{x = 5}}$

Putting x = 5 in Equation ( 1 )

$\implies \sf{3x + 5y = 65}$

$\implies \sf{3 \times 5 + 5y = 65}$

$\implies \sf{5y = 65 - 15}$

$\implies \sf{y = \dfrac{50}{5}}$

$\implies \sf{y = 10}$

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{\red{Price \: of \: a \: pen = Rs.5}}}$

$\large\boxed{\sf{\purple{Price \: of \: a \: book = Rs.10}}}$

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