Question

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 charge for each extra day.

Answer 1

Hint: Consider the fixed charge as ‘x’ and additional charge as ‘y’. Saritha paid Rs. 27 for seven days; additional charge is for 7-3 =4 days. So, $3x + 4y = 27$ as 3 days has fixed charge and 4 days has additional charge for Saritha. Susy paid Rs. 21 for five days; additional charge is for 5-3=2 days. So, $3x + 2y = 21$ as 3 days have fixed charge and 2 days have additional charge for Susy.Solve these two equations to find the answer.


Complete step-by-step solution:
We are given that a lending library has a fixed charge for the first three days and additional charge for each day thereafter. We need to find the fixed charge and charge for each extra day.
Let the fixed charge be ‘x’ and additional charge be ‘y’
Saritha paid Rs. 27 for a book for seven days, 3 days has fixed charge and the remaining 4 days have additional charge.
$3x + 4y = 27$ $ \to eq(1)$
Susy paid Rs. 21 for a book for five days, 3 days has fixed charge and the remaining 2 days have additional charge.
$3x + 2y = 21$ $ \to eq(2)$
By solving equations 1 and 2 we will get the fixed charge and additional charge.
$
  3x + 4y = 27 \\
  3x = 27 - 4y \to eq(3) \\
 $
Substitute eq (3) in eq (2)
$
  3x + 2y = 21 \\
  27 - 4y + 2y = 21 \\
  27 - 2y = 21 \\
  2y = 27 - 21 \\
  2y = 6 \\
  y = \dfrac{6}{2} = 3 \\
 $
Therefore, the additional charge ‘y’ is 3.
Substitute the additional charge value in eq (3) to get the fixed charge.
$
  3x = 27 - 4y \\
  3x = 27 - 4\left( 3 \right) \\
  3x = 27 - 12 \\
  3x = 15 \\
  x = \dfrac{{15}}{3} = 5 \\
 $
Therefore, the fixed charge ‘x’ is 5.


Note: In this question, the linear equations are solved using substitution method. Linear equations with two variables can also be solved using the Graphing method and elimination method.