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in Linear Equations by (65.2k points)

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.

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Best answer

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.

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