Question

37 pen and 53 pencil together cost rs 394, 37pencil and 53 pen together cost 506 .find cost of a pen

Answer 1

let the cost of one pen = x RS.
and, the cost of one pencil= y RS.

case 1st

37x+53y= 394. ------(1)

case 2nd

cost of 53 pen = 53x
cost of 37 pencil= 37 y

ATQ

53x+37y = 506. -----(2)

now,
adding eq (1) and (2)

37x+53y = 394
53x+37y = 506
----------------------
90x+90y = 900

90(x+y) = 900
x+y = 10. ------(3)

now, subtract eq. (1) from (2)

53x+37y = 506
37x+ 53y = 394
(-). (-). . (-)
-----------------------
16x - 16y = 112
=> 16(x-y) = 112
=> x-y = 7 -------- (4)

adding eq (3) and (4)

x+y = 10
x-y = 7
_______
2x = 17
=> x = 17/2
=> x= 8.5

hence the cost of the phone = x = 8.5 rs