Question

Question 2 (v)
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

Answer 1

Let the fixed charge for first three days and each day charge thereafter be Rs x and Rs y respectively.
According to the question,
x + 4y = 27 ... (i)
x + 2y = 21 ... (ii)
Subtracting equation (ii) from equation (i), we get
2y = 6
y = 3 ... (iii)
Substituting the value of y in equation (i), we get
x + 12 = 27
$\Rightarrow$ x = 15
Hence, fixed charge = Rs 15 and charge per day = Rs 3