A lending library has a fixed charge for the first three days and an additional charge for each day thereafter.

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.

Answer 1

Fixed charge be Rs. x. 

Additional charge be Rs. y. 

x + 4y = 27 ………. (i) 

x + 2y = 21 ………. (ii) 

Subtracting Eqn. (ii) from eqn. (i),

Substituting the value of ‘y’ in eqn. (i) 

x + 4y = 27 

x + 4(3) = 27 

x + 12 = 27 

∴ x = 27 – 12 

∴ x = 15 

∴ Fixed charge, x = Rs. 15.

 Additional charge, y = Rs. 3.