Cost of a Pen and a Pencil Box

Video Explanation

Question

The cost of 4 pens and 4 pencil boxes is ₹100. Three times the cost of a pen is ₹15 more than the cost of a pencil box. Form the pair of linear equations and find the cost of a pen and a pencil box.

Solution

Step 1: Let the Variables

Let the cost of one pen = ₹ \(x\)

Let the cost of one pencil box = ₹ \(y\)

Step 2: Form the Equations

Cost of 4 pens and 4 pencil boxes = ₹100

\[ 4x + 4y = 100 \quad (1) \]

Three times the cost of a pen is ₹15 more than the cost of a pencil box:

\[ 3x = y + 15 \]

\[ 3x – y = 15 \quad (2) \]

Step 3: Simplify Equation (1)

Divide equation (1) by 4:

\[ x + y = 25 \quad (3) \]

Step 4: Solve by Elimination Method

Add equation (2) and (3):

\[ (3x – y) + (x + y) = 15 + 25 \]

\[ 4x = 40 \]

\[ x = 10 \]

Step 5: Find the Value of y

Substitute \(x = 10\) in equation (3):

\[ 10 + y = 25 \]

\[ y = 15 \]

Conclusion

Cost of one pen:

\[ \boxed{₹\; 10} \]

Cost of one pencil box:

\[ \boxed{₹\; 15} \]

Final Answer (For Exam)

Cost of one pen = ₹10
Cost of one pencil box = ₹15