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.

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Solution

## Step 1:Form the linear equations.Consider the fixed charge be $₹x$ and the Extra charge be $₹y$As per the question$x+4y=27—\left(1\right)\phantom{\rule{0ex}{0ex}}x+2y=21—\left(2\right)$Step 2:Solve the linear equations.Subtract equation $\left(2\right)$ from equation$\left(1\right)$$x+4y=27\phantom{\rule{0ex}{0ex}}x+2y=21\phantom{\rule{0ex}{0ex}}\left(-\right)\left(-\right)\left(-\right)\phantom{\rule{0ex}{0ex}}...............................\phantom{\rule{0ex}{0ex}}0x+2y=6\phantom{\rule{0ex}{0ex}}...............................\phantom{\rule{0ex}{0ex}}$$⇒2y=6\phantom{\rule{0ex}{0ex}}⇒y=3$putting$y=3$ in equation $\left(1\right)$ we get,$x+4\left(3\right)=27\phantom{\rule{0ex}{0ex}}⇒x+12=27\phantom{\rule{0ex}{0ex}}⇒x=27–12\phantom{\rule{0ex}{0ex}}⇒x=15$Therefore, the fixed charge $=₹15$ and extra charge $=₹3$

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