Question

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

Step 1:Form the linear equations.

Consider the fixed charge be $₹x$ and the Extra charge be $₹y$

As per the question

$$\begin{gathered} x+4y=27—\left(1\right) \\ x+2y=21—\left(2\right) \end{gathered}$$

Step 2:Solve the linear equations.

Subtract equation $\left(2\right)$ from equation$\left(1\right)$

$$\begin{gathered} x+4y=27 \\ x+2y=21 \\ (-)(-)(-) \\ ............................... \\ 0x+2y=6 \\ ............................... \end{gathered}$$

$$\begin{gathered} \Rightarrow 2y=6 \\ \Rightarrow y=3 \end{gathered}$$

putting$y=3$ in equation $\left(1\right)$ we get,

$$\begin{gathered} x+4\left(3\right)=27 \\ \Rightarrow x+12=27 \\ \Rightarrow x=27–12 \\ \Rightarrow x=15 \end{gathered}$$

Therefore, the fixed charge $=₹15$ and extra charge $=₹3$