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.

Answer 1

Let the cost of a pen be Rs x and that of a pencil be Rs y. Then

5x + 6y = 9 ....(i)

3x + 2y = 5 ....(ii)

Multiplying equation (i) by 2 and equation (ii) by 6, we get

10x + 12y = 18 ....(iii)

18x  + 12y = 30 ...(iv)

Subtracting equation (iii) by equation (iv), we get

18x - 10x + 12y - 12y = 30 - 18

=> 8x = 12

`=> x = 12/8 = 3/2 = 1.5`

Substituting x = 1.5in equation (i), we get

5 x 1.5 + 6y = 9

=> 7.5 + 6y = 9

=> 6y = 9 - 7.5

=> 6y = 1.5

=> y = `1.5/6 = 1/4 = 0.25`

Hence, cost of one pen = Rs 1.50 and cost of one pencil = Rs 0.25