#### Question

Form the pair of linear equations in the following problems, and find their solutions (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

#### Solution

Let the fixed charge for first three days and each day charge thereafter be Rs x and Rs y respectively. According to the given information.

x + 4y = 27 ... (1)

x + 2y = 21....(2)

Subtracting equation (2) from equation (1), we obtain

2y = 6

y = 3 ....(3)

Substituting in equation (1), we obtain

x + 12 = 27

x = 15

Hence, fixed charge = Rs 15 And Charge per day = Rs 3