A lending library has a fixed charge for the first three days and… - Vidyadip

Question

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid $₹ 27$ for a book kept for seven days, while Susy paid $₹ 21$ for the book she kept for five days. Find the fixed charge and the charge for each extra day. Solve the pair of the linear equation obtained by the elimination method.

✓

Answer

Suppose the fixed charge be $Rs.\ x$ and the extra charge per day be $Rs\ y$.
According to the question, Mona paid $Rs\ 27$ for a book kept for $7$ days,
$\Rightarrow$ $x + 4y = 27$$........(i)$
Tanvy paid $Rs.\ 21$ for a book kept for $5$ days,
$\Rightarrow$ $x+ 2y = 21$$.........(ii)$
Subtracting $(ii)$ from $(i)$,
$\Rightarrow 2y = 6$
$\Rightarrow$ $y = 3$
Substituting $y = 3$ in $(ii)$, we get $x = 15$
The fixed charge is $Rs.\ 15$ and the charge per day is $Rs\ 3$.

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