Question

A person spent564 in byuing pens and pencils if the cost of each pen is 7 and each pencil cost is 3 and if the total number of things bought was 108 how,many of each type did he buy .

Answer 1

✰ AnSwer:

• He bought 48 pencils and 60 pens

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✒ GiVen :

• Cost of each pen = Rs 7
• Cost of each pencil = Rs 3
• Total number of things bought = 108
• Total cost spent by the person = 564

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✒ To Find :

• Total no. of pen and pencils bought by the person.

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✒ SoluTion :

• Let the no. of pens be x and no. of pencils be y.

According to the question,

$\implies$ x + y = 108-----{1}

$\implies$ 7x + 3y = 564-----{2}

$\implies$ x = 108 - y-----{3}

Now substitute the value of x in eqn (2),

$\implies$ 7x + 3y = 564

$\implies$ 7(108 - y) + 3y = 564

$\implies$ 756 - 7y + 3y = 564

$\implies$ - 4y = 564 - 756

$\implies$ 4y = 192

$\implies$ y = 192/4

$\implies$ y = 48

Similarly,

Substitute the value of y in eqn (3)

$\implies$ x = 108 - y

$\implies$ x = 108 - 48

$\implies$ x = 60

Therefore,

• No. of pens = x = 60
• No. of pencils = y = 48

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✰ Verification :

It is given that total number of things bought by the person are 108.

So,

$\implies$Total things = No. of pencils + No. of pens

$\implies$ 108 = 48 + 60

$\implies$ 108 = 108

$\implies$ LHS = RHS

☯Hence verified!!

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Answer 2

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{ Given }}}}}}$

• Cost of 1 pen = Rs 7
• Cost of 1 pencil = Rs 3
• Total number of things Brought = 108
• Total money spent by the person = 564

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{ To\: find }}}}}}$

• Total no. of pen and pencils bought by the person.

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{solution}}}}}}$

• Let the no. of pens be x and no. of pencils be y.

According to the question,

$\implies$ x + y = 108-----{i}

$\implies$ 7x + 3y = 564-----{ii}

$\implies$ x = 108 - y-----{iii}

• Now put the value of x in eqn (ii),

$\implies$ 7x + 3y = 564

$\implies$ 7(108 - y) + 3y = 564

$\implies$ 756 - 7y + 3y = 564

$\implies$ - 4y = 564 - 756

$\implies$ 4y = 192

$\implies$ y = 192/4

$\implies$ y = 48

Similarly,

Substitute the value of y in eqn (iii)

$\implies$ x = 108 - y

$\implies$ x = 108 - 48

$\implies$ x = 60

Therefore,

No. of pens = x = 60

No. of pencils = y = 48

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{Answer }}}}}}$

He bought 48 pencils and 60 pens