Cost of One Pen and One Pencil

Video Explanation

Question

5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of 1 pen and 1 pencil.

Solution

Step 1: Let the Variables

Let the cost of 1 pen = Rs \(x\)

Let the cost of 1 pencil = Rs \(y\)

Step 2: Form the Equations

\[ 5x + 6y = 9 \quad (1) \]

\[ 3x + 2y = 5 \quad (2) \]

Step 3: Solve by Elimination Method

Multiply equation (2) by 3:

\[ 9x + 6y = 15 \quad (3) \]

Subtract equation (1) from (3):

\[ (9x + 6y) – (5x + 6y) = 15 – 9 \]

\[ 4x = 6 \]

\[ x = \frac{3}{2} \]

Step 4: Find the Value of y

Substitute \(x = \frac{3}{2}\) in equation (2):

\[ 3\left(\frac{3}{2}\right) + 2y = 5 \]

\[ \frac{9}{2} + 2y = 5 \]

\[ 2y = \frac{1}{2} \]

\[ y = \frac{1}{4} \]

Conclusion

Cost of 1 pen:

\[ \boxed{Rs\; \frac{3}{2}} \]

Cost of 1 pencil:

\[ \boxed{Rs\; \frac{1}{4}} \]