Question

A three-wheeler scooter charges Rs. 10 for the first kilometer and Rs. 4.50 each for every subsequent kilometer. For a distance of x km, an amount of Rs. y is paid. Write the linear equation representing the above information.

Answer 1

As,

For every first kilometer the scooter charges Rs 10.

For every subsequent kilometer the scooter charges Rs 4.50 each.

To find a distance of x km, an amount of Rs y is paid.

Therefore,

x km can be written as

x = 1 + (x $-$ 1)

The price paid for x km is y can be written as

$$\begin{gathered} y=10+4.50\left(x-1\right) \\ \Rightarrow y=10+\frac{9}{2}\left(x-1\right) \\ \Rightarrow 2y=20+9\left(x-1\right) \\ \Rightarrow 2y=20+9x-9 \\ \Rightarrow 9x-2y+11=0 \end{gathered}$$

So, the linear equation representing the given information is 9x $-$ 2y + 11 = 0.