Question

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Answer 1

Let the fixed charge for the first three days and each day charge thereafter be Rs x and Rs y, respectively.

According to the question,

x + 4y = 27              ...(1)

The charge for keeping a book for five days is ₹ 2.

x + 2y = 21             ...(2)

By subtracting equation (2) from equation (1)

(x + 4y = 24) - (x + 2y = 21)

y = 3

Putting the value of y in equation (1)

x = 15

Hence, the fixed charge is ₹ 15 and the charge for the additional day is ₹ 3.