Cost of Bags and Pens

Video Explanation

Question

3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost Rs 324. Find the total cost of 1 bag and 10 pens.

Solution

Step 1: Let the Variables

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

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

Step 2: Form the Equations

\[ 3x + 4y = 257 \quad (1) \]

\[ 4x + 3y = 324 \quad (2) \]

Step 3: Solve by Elimination Method

Multiply equation (1) by 4:

\[ 12x + 16y = 1028 \quad (3) \]

Multiply equation (2) by 3:

\[ 12x + 9y = 972 \quad (4) \]

Subtract (4) from (3):

\[ 7y = 56 \]

\[ y = 8 \]

Step 4: Find the Value of x

Substitute \(y = 8\) in equation (1):

\[ 3x + 4(8) = 257 \]

\[ 3x + 32 = 257 \]

\[ 3x = 225 \]

\[ x = 75 \]

Step 5: Find Required Cost

\[ x + 10y = 75 + 10(8) \]

\[ = 75 + 80 \]

\[ = 155 \]

Conclusion

Total cost of 1 bag and 10 pens:

\[ \boxed{Rs\;155} \]