Question

7. If 37 pens and 53 pencils together cost Rs. 320, while 53 pens and 37 pencils together cost Rs. 400. Find the cost of a pen and that of a pencil.

Answer 1

let the value of pen be x
let the value if pencil be y
37x+53y=320..........(1)
53x+37y=400..............(2)
on multiplying eq-1 by 53 and eq-2 by 37
1961x+2809y=16960
1961x+1369y=14800
on subtracting
1440y=2160
y=Rs1.5
so x=
37x+53*1.5=320
37x+79.5=320
37x=320-79.5
37x=240.5
x=Rs6.5
so cost of pen is Rs 6.5 and cost of pencil is Rs 1.5

Answer 2

Hello dear friend ...
☺☺ _ SOLUTION _ ☺☺
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Let the cost of each pen be ₹ x
and that of a pencil be ₹ y .

Than ,
$37x + 53y = 320 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .. ....(1) \\ and \: \: 53x + 37y = 400 \: \: \: \: \: \: \: \: \: .......(2)$

Adding (1) and (2) , we get
$90x + 90y = 720 \\ = > 90(x + y) = 720 \\ \\ = > x + y = \frac{720}{90} = 8 \\ \\ = > x + y = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ........(3)$

ON subtracting (1) from (2) ,


53x + 37y = 400
37x + 53y = 320
(-) (-) (-)
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16x - 16y = 80
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we get,

$16x - 16y = 80 \\ = > 16(x - y) = 80 \\ \\ = > x - y = \frac{80}{16} = 5 \: \: \: \: \: \: \: \: \: \: \: ........(4)$


Adding (3) and (4) , we get

$2x = 13 \\ = > x = \frac{13}{2} = 6.5$


Subtracting (4) from (3) ,

we get

$= > 2y = 3 \\ \\ = > y = \frac{3}{2} = 1.5$


So ,

Cost of each pens = ₹ 6.5
and cost of each pencils = ₹ 1.5

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Hope it's helps you.
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