Question

5 pencils and 7 pens together cost Rs.50 whereas 7 pencils and 5 pens

together costs Rs 50. The cost of 1 pen is​

Answer 1

Let :

• Cost of one pencil = x Rs
• Cost of one pen = y Rs

Given :

• 5 pencils and 7 pens cost Rs 50
• 7 pencils and 5 pens costs Rs 50

To find :

Cost of one pen

Solution :

First of all form linear equation.

1) 5 pencils and 7 pens cost Rs 50

➝ 5x + 7y = 50 ....... equation 1

2) 7 pencils and 5 pens costs Rs 50

➝ 7x + 5y = 50 ..... Equation 2

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Multiply equation 1 by 7 and equation 2 by 5

7(5x + 7y = 50)

➝ 35x + 49y = 350 ........ equation 3

5(7x + 5y = 50)

➝ 35x + 25y = 250....... equation 4

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Subract equation 4 from equation 3

➝(25x + 49y) - (35x + 25y) = 350 - 250

➝ (35x - 35x) + (49y - 25y) = 100

➝ 24y = 100

➝ y = 100/24

➝ y = 25/6

Cost of one pen (y) = (25/6) Rs

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ANSWER : Rs(25/6)

Answer 2

${\underline{\underline{\bf{Given :}}}}$

• 5 Pencils and 7 pens Cost = Rs 50
• 7 pencils and 5 pens Cost = Rs 50

${\underline{\underline{\bf{To \: \: find :}}}}$

• Cost of One pen

${\underline{\underline{\bf{Assumption :}}}}$

• Cost of one pencil be x
• Cost of one pen be y.

${\underline{\underline{\bf{Solution :}}}}$

❂ Making the Equation

• 5x + 7y = 50 ........(eq - 1)
• 7x + 5y = 50 ........(eq - 2)

❂Here from equation 1 we get :-

$\sf{ \implies{5x + 7y = 50}}$

$\sf{ \implies{5x= 50 - 7y}}$

$\sf{ \implies{x= \cfrac{ 50 - 7y}{5}}}$

❂ Putting the unknown value of x in equation 2 we to get the value y :-

${ \sf{ \implies{7x + 5y = 50}}}$

${ \sf{ \implies{7 \bigg( \cfrac{50 - 7y}{5} \bigg) + 5y = 50}}}$

${ \sf{ \implies{ \cfrac{350 - 49y}{5} + 5y = 50}}}$

${ \sf{ \implies{ \cfrac{350 - 49y + 25y}{5} = 50}}}$

${ \sf{ \implies{ \cfrac{350 - 24y}{5} = 50}}}$

${ \sf{ \implies{ {350 - 24y} = 50 \times 5}}}$

${ \sf{ \implies{ {350 - 24y} =250}}}$

${ \sf{ \implies{ - 24y=250 - 350}}}$

${ \sf{ \implies{ - 24y= - 100}}}$

${ \sf{ \implies{ 24y=100}}}$

${ \sf{ \implies{ y= \cfrac{100}{24}}}}$

${ \sf{ \implies{ y= \cfrac{25}{6}}}}$

$\large{ \underline{ \overline{ \boxed{ \bf{ \implies{ y= 4.17}}}}}}$

Here y = 4.17 which is the cost of one pen as we had considered the cost of one pen be y. So, Cost of one pen is 4.17 Rs.