Question

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 number of pens be 'x' and the number of pencils be 'y'
Therefore 37x + 53y = 320 ---1
53x +37y = 400 ----2
Now, adding both the equations,
90x + 90y = 720 (dividing the whole equation by 90 )
X + y = 8 -----3
Now subtracting both the euations,
-16x +16y = -80 (dividing the equation by 16)
-x +y = -5 ---4
Adding 3 and 4
2y=3
Y=3/2
Y= 1.5rs
Therefore x = 13/2
X=6.5rs

Answer 2

$\huge{\boxed{\mathbb{ANSWER}}}$

Given :

IN Ist CASE

Number of pens = 37

Number of pencils = 53

Together cost = Rs 320

IN IInd CASE

Number of pens = 53

Number of pencils = 37

Together cost = Rs 400

To find : The cost of a pen and that of a pencil.

Let the cost of the pen be Rs " x "and

That of pencil be Rs " y ".

Then, According to given question

37x + 53y = 320  --------- ( i )

and, 53x + 37y = 400  ------ ( ii )

Now we are , Adding the equations (i) and (ii)

Then we get :

90x + 90y = 720 ⇒ x + y = 8    ----- ( iii )

Now subtract eq ( i ) and ( ii ) ,

We get :

16x - 16y =  80 ⇒ x - y = 5   ----------- ( iv )

Add equation  ( iii ) and  ( iv )

We get :

2x = 13 ⇒ x = 6.5

$\implies \boxed{\mathsf{x\:=\:6.5}}$

Subtract x = 6.5 in equation ( iii ) ,

We get :

y = ( 8 - 6.5 )

$\implies \boxed{\mathsf{y\:=\:1.5}}$

ATLAST, I AM GOING TO CONCLUDE THE WHOLE ANSWER!

$\huge{\boxed{\sf{Cost\:Of\:One\:Pen\:=\:Rs\:6.50.}}}$

And

$\huge{\boxed{\sf{Cost\:Of\:One\:Pencil\:=\:Rs\:1.50.}}}$