Question

The cost of 2pencils and3 rubbers is 9₹ and the cost of 3pencils and 6 rubbers is₹15.find the cost of each pencil and rubber
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Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• 2 pencils and 3 rubbers cost = Rs. 9
• 3 pencils and 6 rubbers cost = Rs. 15

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Cost of 1 pencil = ??
• Cost of 1 rubber = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

• Let cost of 1 pencil be x
• Let cost of 1 rubber be y

Acc. to 1st statement :-

⠀⠀⠀⠀

2x + 3y = 9 ----- ( i )

⠀⠀⠀⠀

Acc. to 2nd statement :-

⠀⠀⠀⠀

3x + 6y = 15

⠀⠀⠀⠀

3 ( x + 2y ) = 15

⠀⠀⠀⠀

x + 2y = 15 / 3

⠀⠀⠀⠀

x + 2y = 5 ------- ( ii )

⠀⠀⠀⠀

• Multiply eq ( ii ) by 2

⠀⠀⠀⠀

2x + 4y = 10 ---- ( iii )

⠀⠀⠀⠀

• Subtracting eq ( i ) from ( iii )

⠀⠀⠀⠀

2x + 4y - 2x - 3y = 10 - 9

⠀⠀⠀⠀

4y - 3y = 10 - 9

⠀⠀⠀⠀

y = 1

⠀⠀⠀

⠀⠀⠀⠀

• putting value of y in eq ( i )

⠀⠀⠀⠀

2x + 3y = 9

⠀⠀⠀⠀

2x + 3 × 1 = 9

⠀⠀⠀⠀

2x = 9 - 3

⠀⠀⠀⠀

2x = 6

⠀⠀⠀⠀

x = 6 / 3

⠀⠀⠀⠀

x = 2

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Cost of 1 pencil = x = Rs. 2
• Cost of 1 rubber = y = Rs. 1

Answer 2

Given:

• Cost of 2pencils and 3rubbers = ₹ 9
• Cost of 3pencils and 6rubbers = ₹ 15

Find:

• Cost of each pencil and rubber

Solution:

Let, cost of pencil as ₹ x

and cost of rubbers as ₹ y

Now,

$\mathbb{ACCORDING \: TO \: QUESTION}$

➢ 2x + 3y = ₹ 9 ........(1)

➢ 3x + 6y = ₹ 15 .......(2)

Taking eq(1)

$\sf \to 2x + 3y = 9$

$\sf \to 2x = 9 - 3y$

$\sf \to x = \dfrac{9 - 3y}{2}$

________________

Now, use this value of x in eq(2)

$\sf \to 3x + 6y = 15$

$\sf \to 3( \dfrac{9 - 3y}{2}) + 6y = 15$

$\sf \to \dfrac{27- 9y}{2} + 6y = 15$

$\sf \to \dfrac{27- 9y + 12y}{2}= 15$

$\sf \to \dfrac{27 + 3y}{2}= 15$

$\sf \to 27 + 3y= 15 \times 2$

$\sf \to 27 + 3y= 30$

$\sf \to 3y= 30 - 27$

$\sf \to 3y= 3$

$\sf \to y = \cancel{ \dfrac{3}{3} } = 1$

$\sf \to y = 1$

So, y = 1

________________

Now, put value of y in eq(1)

$\sf \to 2x + 3y = 9$

$\sf \to 2x + 3(1) = 9$

$\sf \to 2x + 3 = 9$

$\sf \to 2x= 9 - 3$

$\sf \to 2x= 6$

$\sf \to x = \cancel{ \dfrac{6}{2} } = 3$

$\sf \to x = 3$

So, x = 3

________________

Hence, x = ₹3

y = ₹1

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VERIFICATION

$\sf \to 2x + 3y = 9$

$\sf \to 2(3) + 3(1) = 9$

$\sf \to 6+ 3= 9$

$\sf \to 9= 9$

Here,

L.H.S = R.H.S

Hence, Verified