Activity 1: Finding Out Charges For Postal Parcels

Express Parcel:

We will look at the charges for Express Parcel.
The tariff table below has various categories for the charges.

We will form equations and graphs based on this data; it will help us calculate the amount to be paid for a given parcel.

Let us consider the first category:

Local Upto 500 gms.

This means that if the parcel is to be delivered within the city and the weight of the parcel is less than 500 gms, then the charges would be Rs. 30. These are the minimum charges that we have to pay for the parcel. Let us write an equation for this, if C are the charges then, for this case C = 30.
 

Local Above 500 gms:

Now, if our weight is larger than 500 gms., then we have to add Rs. 8 for each 500 gms. For example, if our parcel weighs 1.3 kg or 1300 gms. Then we have additional 800 gms above the first 500 gms. That is 500 gms + 300 gms. Hence we have to add Rs. 16 (8+8) for this extra weight. Thus our charges become
 

C = 2 x 8 + 30

Our weight can keep on increasing for each 500 gms, we can write this with another variable, lets say w. Our equation hence becomes:
 

C = 8 x w + 30

where w is the number of 500 gms in the weight. This is applicable only when we have weight more than 500 gms. Before that we have a flat rate of Rs. 30.

For example, if our parcel weights 3.2 Kilograms. This is 2.7 kgs above the first 500 gms. Then we calculate, how many number of 500 gms are in 2700 gms. We can write it as
 

500 + 500 + 500 + 500 + 500 + 200 = 2700

Hence after rounding we have 6 units of 500 gms. Hence our charges are
 

C = 8 x 6 + 30 = 48 + 30 = 78

Local Above 5 kg:

This is the third category. In this case the fixed charges would be Rs 30 + 9 x 8 = 102. (9 is from 4.5 kg = 500 gm x 9) Any weight above 5 kg is charged Rs. 10 for each 500 gms. So our equation becomes:
 

C = 10 x w + 102

where w is the number of 500 gms weight, above 5 kg.

For example, if our parcel weighs 8.3 kgs then how do we calculate the charges.

We have 8.3 kg = 5 kg + 3.3 kg. For 5 kg. the charges are Rs. 102.
So we have to calculate the extra charges for 3.3 kgs. For 3.3 kgs = we have 7 units of 500 gms.

Hence the total charges are C = 10 x 7 + 102 = 70 + 102 = Rs. 172

Next we will see how to represent these equations graphically for easily finding the charges.