Question

An auto charges Rs.15 for first kilometre and Rs.8 each for subsequent kilometre. For a total distance of ‘x’ km an amount of Rs. ‘y’ is said. Write the linear equation representing this information
a) y = 8x + 7
b) y = 8x – 7
c) y = 8x + 15
d) None of these

Answer 1

Hint: Distance travelled by auto is x, for 1km is Rs.15. Thus the rest will be (x – 1) on each for Rs.8. Total amount is y, thus from the linear equation for y as the sum of distance travelled by the auto.

It is said that an auto charge Rs.15 for 1st kilometre and Rs.8 each for each subsequent km. Now it is said that auto travel ‘x’ km, this means that for a distance of x km, Rs.15 is paid for the first km and Rs.8 paid for the rest of the km.
Now, out of ‘x’ km already 1km is travelled and we know the amount as Rs.15, thus the rest of the travel will be (x – 1) km.
It is said that the total amount is ‘y’ rupees, thus the total will be Rs.15 for first km and RS.8 for (x – 1) km. Thus the total amount paid is y and the equation will be,
y = 15 + 8 (x-1)
Now, let us simplify the given expression,
y = 15 + 8x – 8
y = 8x + 7
Thus we got the linear equation representing the equation as,
y = 8x + 7
Therefore option (a) is the correct answer.

Note: If you assume values for (x. y) in equation y = 8x + 7, you can find the cost and distance travelled by auto.

X	0	1	2	3
y	7	5	23	31

Thus y = 8x +7
Now if auto travel 1 km, then x = 1.
$\therefore y=8\times 1+7=Rs.15$
If auto travels 2km, then x = 2.
$y=8\times 2+7=16+7=Rs.23$