Question

3 pens and 4 books together cost rs 50 as 5 pens and 3 books together cost rs 54

Answer 1

$\Large{\underline{\underline{\mathfrak{Correct \: Question :}}}}$

3 pens for books together cost ₹50 where 5 pens and 3 books together cost ₹54.Find the value of each pen and book

$\Large{\underline{\underline{\mathfrak{Answer :}}}}$

Given:

$\qquad\qquad$ • Cost of 3 pens and 4 books = ₹50

$\qquad\qquad$ • Cost of 5 pens and 3 books = ₹56

To Find:

$\qquad\qquad$ • Cost of each pen and each book

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Solution:

☯ Let the cost of Pens and Books, x and y respectively.Now we will apply, Elimination method to solve the question.

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$\large\underline{\dag \: {\mathbf{ According \: to \: the \: question:-}}}$

$\qquad$ • The equation that will form are :

$\qquad\qquad\ : \implies\sf\ 3x + 4y = 50 \: - \: \left( eq.1 \right)$

$\qquad\qquad\implies\sf\ 5x + 3y = 56 \: - \: \left( eq.2 \right)$

$\qquad$ • Multiplying (eq.1) by 5 and (eq.2) by 3 :

$\qquad\qquad\ : \implies\sf\ 5 \times \: \left( 3x + 4y = 50 \right)$

$\qquad\qquad\ : \implies\sf\ 15x + 20y = 250 \: - \: \left(eq.3 \right)$

$\qquad\qquad\ : \implies\sf\ 3 \times \: \left(5x + 3y = 56 \right)$

$\qquad\qquad\ :\implies\sf\ 15x + 9y = 168 \: - \: \left(eq.4 \right)$

$\qquad$ • Now,subtract the (eq.3) from (eq.4),i.e. (eq.3) - (eq.4):

$\qquad\qquad\ :\implies\sf\:\cancel{15x} + 20y = 250 \: - \: \left(eq.3 \right)$

$\qquad\qquad\ :\implies\sf\: (-) \cancel{15x} + (-) 9y = 168 \: - \: \left(eq.4 \right)$

$\qquad\qquad\sf\ : \implies\ 11y = 88$

$\qquad\qquad\sf\ : \implies\ y = \frac{\cancel{11}}{\cancel{11}}$

$\qquad\qquad\ : \implies{\underline{\boxed{\mathsf{\red{y = 8}}}}}$

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$\qquad$ • Now,put the the value of y in (eq.1)

$\qquad\qquad\sf\ : \implies\: 3x + 4(8) = 50$

$\qquad\qquad\sf\ : \implies\: 3x + 32 = 50$

$\qquad\qquad\sf\ : \implies\: 3x = 50 - 32$

$\qquad\qquad\sf\ : \implies\: 3x = 18$

$\qquad\qquad\sf\ : \implies\: x = \frac{18}{3}$

$\qquad\qquad\ : \implies{\underline{\boxed{\mathsf{\red{ x = 6 }}}}}$

$\therefore\:\underline{\textsf{Hence, \: the \: cost \: of \: each \: pen and \: book \: is \textbf{6,8}}}$