Question

5 pencils and 7 pens together cost 50 where a 7 pencils and 5 pens together cost 46 then the cost of 1 pencil is

Answer 1

✬ One pen = Rs 5 ✬

✬ One pencil = Rs 3 ✬

Step-by-step explanation:

Given:

• 5 pencils and 7 pens together cost Rs 50.
• 7 pencils and 5 pens together cost Rs 46.

To Find:

• What is the cost of 1 pencil ?

Solution: Let cost of one pencil and one pen be Rs a and b respectively.

[ In first condition ]

➨ Cost of 5 pencil & 7 pens is Rs 50.

➨ 5a + 7b = 50

➨ 5a = 50 – 7b

➨ a = 50 – 7b/5.........(1)

[ In second condition ]

➨ Cost of 7 pencils & 5 pens is Rs 46.

➨ 7a + 5b = 46

➨ 7a = 46 – 5b..........(2)

Now, Put the value of 'a' in equation 2 from 1.

$\implies{\rm }$ 7a = 46 – 5b

$\implies{\rm }$ 7(50 – 7b/5) = 46 – 5b

$\implies{\rm }$ 350 – 49b/5 = 46 – 5b

$\implies{\rm }$ 350 – 49b = 5(46 – 5b)

$\implies{\rm }$ 350 – 49b = 230 – 25b

$\implies{\rm }$ 350 – 230 = – 25b + 49b

$\implies{\rm }$ 120 = 24b

$\implies{\rm }$ 120/24 = b

$\implies{\rm }$ 5 = b

Hence,

➣ Cost of one pen is b = Rs 5.

➣ Cost of one pencil is a = (50b – 7b/5)

=> {50 – 7(5)/5}

=> (50 – 35/5)

=> 15/5 = Rs 3

Answer 2

QUESTION:

5 pencils and 7 pens together cost 50 where a 7 pencils and 5 pens together cost 46 then the cost of 1 pencil is

ANSWER:

Let the cost of one pencil be $\red{ x }$

and the cost of one pen be $\blue {y}$

$\red {According to question:}$

Case 1 :

$5x + 7y = 50.......(eq.1)$

Case 2 :

$7x + 5y = 46......(eq.2)$

Now adding both the equation : Equation 1 and 2;

$(5x + 7y) + (7x + 5y) = 50 + 46 \\ 5x + 7x + 7y + 5y = 96 \\ 12x + 12y = 96 \\ (taking \: 12 \: as \: common) \\ 12(x + y) = 96 \\ x + y = 8 \\ so \: x + y = 8.....(eq.3)$

now subtracting eq 1 and 2;

$(5x + 7y) - (7x + 5y) = 50 - 46 \\ 5x + 7y - 7x - 5y = 4 \\ 5x - 7x + 7y - 5y = 4 \\ - 2x + 2y = 4 \\ (taking \: - 2 \: common) \\ - 2( x - y) = 4 \\ x - y = - 2 \\ so. \: x - y = - 2.....(eq.4)$

adding eq. 3 and 4. ;

$(x + y) + (x - y) = 8 + ( - 2) \\ x + x + y - y = 8 - 2 \\ 2x = 6 \\ x = 3$

hence the cost of one pencil is ruppes 3.

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