Question

5 pencils and 7pens together cost 50 ,whereas 7 pencils and 5 pens together cost 46 .find the cost of one pencils and that of one pen

Answer 1

Answer

• Cost of one pencil = 3 rupees and cost of one pen = 5 rupees.

Given

• The cost of 5 pencils and 7 pen = 50 rupees.
• The cost of 7 pencils and 5 pen = 46 rupees.

To Find

• The cost of one pencil and one pen.

Step By Step Explanation

Assumption :

Let us consider the cost of one pencil be x and cost of one pen be y.

Equation :

Then the equation will be -

$\tt \red{5x + 7y = 50} \: and \: \purple{7x + 5y = 46}$

Solution of Equation :

• Step 1.

Multiplying first equation by 7 and second equation by 5.

$\longmapsto \tt7(5x + 7y = 50) \\ \pink {\implies{35x + 49y = 350}} \\ \\ \longmapsto \tt5(7x + 5y = 46) \\ \green{\implies 35x + 25y + 230}$

• Step 2.

Now, let's subtract to find the value.

$\tt35x \: \: \: + \: \: \: 49y \: \: \: = 350 \\\tt35x \: \: \: +\: \:\: 25y\:\:\:= 230 \\ ( - ) \: \: \: \: \:( - ) \: \: \:\: ( - ) \: \: \: \: \: \\ - - - - - - - - \\\bf 24y = 120$

y = 120/24 => y = 5

Substituting the value of y.

=> 5x + 7y = 50

=> 5x + 7(5) = 50

=> 5x = 50 - 35

=> 5x = 15

=> x = 15/5 => x = 3

Therefore, cost of one pencil = 3 rupees and cost of one pen = 5 rupees.

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