Raman purchases 2 pens and 3 pencils and pays ₹36 to the shopkeeper. Her friend Siya purchases 3 pens and 2 pencils and pays ₹49. What is the cost of one pen?
Answer & explanation
Correct answer: option 2
Raman purchases 2 pens and 3 pencils for ₹36: 2x+3y =36
Siya purchases 3 pens and 2 pencils for ₹49: 3x+2y =49
Now, we have a system of linear equations:
2x+ 3y =36
3x+2y =49
Multiply the first equation by 3 and the second equation by 2:
This gives us:
6x+9y = 108
6x+4y = 98
Next, subtract the second equation from the first to eliminate x
(6x +9y) − (6x +4y) = 108−98
5y =10
y = 2
Now that we have y =2, we can substitute this value into 2x+ 3y=36
2x +3(2) = 36
2x +6 = 36
x =15