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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. I want to know that which method will be best to evaluate this linear equation and it can be solved with that method. Its urgent please give me the answer today.
Let the cost of a pen and cost of a pencil be Rs x and Rs y respectively.
It is given that 37 Pens and 53 pencils together cost Rs. 320.
So, 37x + 53y = 320 (1)
It is also given that 53 Pens and 37 Pencils together cost Rs. 400.
So, 53x + 37y = 400 (2)
Equations (1) and (2) can be solved in any of the method such as: elimination method, substitution method or cross multiplication method.
There is another way of solving equations of the form ax + by = c and bx + ay = d. Add and subtract these two equations and reduce these equations to the standard form. Let these equations be (3) and (4). Now, equations (3) and (4) can be easily solved to obtain x and y.
Adding and subtracting equations (1) and (2);
37x + 53y + 53x + 37y = 320 + 400 and 37x + 53y  53x  37y = 320  400
OR, 90x + 90y = 720 and 16x + 16y = 80
OR, 90(x + y) = 720 and 16(x  y) = 80
OR, x + y = 8 (3)
And x  y = 5 (4)
Adding (3) and (4); 2x = 13
OR, x = 6.5
Substituting the value of x in equation (3); y = 1.5
Therefore, the cost of a pen and a pencil are Rs 6.5 and Rs 1.5 respectively.