Question

The parking charges of a vehicle in a shopping center is Rs. 40 for first 2 hours and Rs. 5 for each subsequent hour. Write an equation for 8 hours.

Answer 1

Hint: In order to find out the equation assume the total charges to be paid and the total hours for which the vehicle is parked as some unknown variables. Further use the problem statement to form the equation.

Complete step-by-step answer:
Given that:
Parking charges for first 2 hours = Rs. 40
Parking charges for rest of the hours = Rs. 5
Let us assume total parking time = x hour
And total charge to be paid =Rs. y
So, the total charge to be paid will be charged for the first two hours and the charge for left hours.
\[ \Rightarrow {\text{Total charges }} = {\text{ }}\left( {{\text{Total hours }} - 2} \right) \times Rs.5{\text{ }} + {\text{ }}Rs.{\text{ }}40\]
As we have assumed total charge to be y and total hours to be x so substituting in the above equation we get:
$\therefore y = \left( {x - 2} \right) \times Rs.5 + Rs.40$
In order to find the equation for 8 hours we will replace x by 8.
$
  \therefore y = \left( {8 - 2} \right) \times Rs.5 + Rs.40 \\
   \Rightarrow y = \left( 6 \right) \times Rs.5 + Rs.40 \\
  y = Rs.30 + Rs.40 = Rs.70 \\
 $
Hence the equation for 8 hours is $ = \left( {8 - 2} \right) \times Rs.5 + Rs.40$ and the parking charges for 8 hours is Rs.70.

Note: For solving such a type of question where different charges are assigned for different hours try to find the net charge by dividing the total hours in different blocks of hours, finding the charges for each block separately and finally the sum at the end. These types of problems can be solved easily by the use of algebra.