LINEAR EQUATIONS

Activity 1: Finding Charges for Parcels

Express Parcel:

We will look at the charges for Express Parcel. The tariff table below has various categories of 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 - Up to 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 parcels. Let us write an equation for this, if C is the charge then, C = 30.
 

Local - Above 500 gms
 

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

C = 8 x 2 + 30

Our weight can keep on increasing for every additional 500 gms. We can represent the number of additional 500 gms with another variable, let us say w. Our equation now becomes:

C = 8 x w + 30

This equation is applicable only when we have weight more than 500 gms. Before that, we have a flat rate of Rs. 30.


Taking another example of parcel weight 3.2 Kgs. This is 2.7 kgs above the first 500 gms. We calculate the number of 500 gms in 2700 gms. We can write 2700 as:

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

Hence, after rounding we have 6 units of additional 500 gms. Hence the charge will be calculated as:

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

Local - Above 5 kg

In this category, the fixed charges would be 30 + 9 x 8 = Rs. 102. (9 comes from an additional 4.5 kg = 500 gm x 9) Any weight above 5 kg is charged Rs. 10 for every subsequent 500 gm thereafter. So our equation becomes:

C = 10 x w + 102

, where w is the number of additional 500 gms 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 kgs, the charges are fixed as Rs. 102.
So, we have to calculate the charges for the additional 3.3 kgs. For 3.3 kgs = we have 7 units of 500 gms.

Hence, the total charge is C = 10 x 7 + 102 = 70 + 102 = Rs. 172.

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