Cost of Books and Pens

Video Explanation

Question

5 books and 7 pens together cost Rs 79 whereas 7 books and 5 pens together cost Rs 77. Find the total cost of 1 book and 2 pens.

Solution

Step 1: Let the Variables

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

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

Step 2: Form the Equations

\[ 5x + 7y = 79 \quad (1) \]

\[ 7x + 5y = 77 \quad (2) \]

Step 3: Solve by Elimination Method

Multiply equation (1) by 7:

\[ 35x + 49y = 553 \quad (3) \]

Multiply equation (2) by 5:

\[ 35x + 25y = 385 \quad (4) \]

Subtract (4) from (3):

\[ 24y = 168 \]

\[ y = 7 \]

Step 4: Find the Value of x

Substitute \(y = 7\) in equation (1):

\[ 5x + 49 = 79 \]

\[ 5x = 30 \]

\[ x = 6 \]

Step 5: Find Required Cost

\[ x + 2y = 6 + 2(7) \]

\[ = 6 + 14 \]

\[ = 20 \]

Conclusion

Total cost of 1 book and 2 pens:

\[ \boxed{Rs\;20} \]