Grade 12 Mathematical Literacy: Tariffs

Summary

This educational video aims to demystify water tariffs for students, teaching them how to calculate charges based on usage. The host explains the concept of tariffs and breaks down the billing system into understandable segments, using a tiered pricing structure example. They walk through calculations for different levels of water consumption, illustrating how costs escalate with usage. The video also addresses how to compare tariffs between levels, providing a practical example to determine the financial impact of different billing rates.

Takeaways

• 📚 The channel's focus is on helping struggling math students become proficient in mathematics.
• 📅 New videos are posted on Tuesdays and Thursdays, with an emphasis on subscribing and turning on notifications for updates.
• 💧 The video specifically addresses water tariffs, a complex section of tariffs that often carries significant marks in exams.
• 🔢 A tariff is a billing system used by service providers to determine how customers are charged for goods or services.
• 🏠 Water tariffs are charged per kiloliter, with a kiloliter being equivalent to a thousand liters.
• 📊 The cost of water increases with usage, with different rates for different ranges of kiloliters used.
• 🧮 The video provides a step-by-step guide on how to calculate water tariffs using a given table.
• 📘 Examples are given to illustrate the calculation process for households using different amounts of water.
• 𑁍 The first six kiloliters of water are charged at a standard rate, regardless of the total amount used.
• 📝 The video explains how to calculate the difference in charges between two different tariff levels for a given water usage.
• 📚 Encourages viewers to practice the calculation process independently by pausing the video and working through the examples without looking at the provided answers.

Q & A

What is the primary purpose of the video?

The primary purpose of the video is to teach viewers how to understand and calculate water tariffs, focusing on the concept of tiered pricing for water usage.

What are the days when new videos are posted on the channel?

New videos are posted on Tuesdays and Thursdays.

What is a tariff in the context of the video?

A tariff, in this context, refers to a billing system used by service providers to determine how customers are charged for goods or services, such as water usage.

How is water generally charged to households?

Water is generally charged per kiloliter, with different rates applying depending on the amount of water used.

What is a kiloliter and how does it relate to water billing?

A kiloliter is a unit of volume equal to one thousand liters. It is used in water billing to measure the amount of water a household uses and to determine the cost.

How does the cost of water change with usage in the example provided?

The cost of water increases with usage, with different price points for different ranges of kiloliters used. The more water used, the higher the unit price for the additional water.

Can you explain the calculation for a household that uses 5 kiloliters of water based on the video?

For a household using 5 kiloliters, the cost is calculated by multiplying the rate per kiloliter (4.65) by the amount used (5), resulting in a total cost of 23 Rand and 25 cents.

What is the significance of the first 6 kiloliters in the water tariff system described?

The first 6 kiloliters are charged at a standard rate regardless of the total amount used. This base rate applies to all households, and additional usage is charged at higher rates.

How does the video suggest practicing the understanding of water tariffs?

The video suggests pausing the video at the point where the question and table are shown, and then attempting to calculate the costs without looking at the provided answers to reinforce learning.

What type of question might be asked in an exam regarding water tariffs?

An exam question might ask to calculate the cost difference between two different tariff levels for a given amount of water usage, such as comparing level one and level two tariffs for 19 kiloliters.

What is the final step in the exam question example provided in the video?

The final step is to calculate the total cost for both level one and level two tariffs for 19 kiloliters of water usage and then determine the difference in cost between the two levels.

Outlines

00:00

📚 Introduction to Math Mastery and Water Tariffs

The video script introduces a channel dedicated to transforming struggling math students into math masters, with new content posted on Tuesdays and Thursdays. The focus of this video is on tariffs, specifically water tariffs, which are complex and often award the most marks in exams. The script provides a basic definition of a tariff as a billing system used by service providers to charge customers for goods or services. The example of water tariffs is used to illustrate the concept, explaining that water is charged per kiloliter and that understanding this billing system is key to grasping other types of tariffs.

05:01

💧 Calculating Water Tariffs with Examples

This paragraph delves into the specifics of calculating water tariffs, using a table to demonstrate how charges are applied based on the volume of water used. The script explains that the first six kiloliters are charged at a standard rate, and any usage beyond this initial amount is charged at an increased rate, depending on the range of usage. Detailed calculations are provided for households using 5, 8.3, and 13 kiloliters, showing how to apply the tariff rates to determine the total cost. The importance of understanding the pricing tiers and calculating the exact charges for each tier is emphasized.

10:04

📘 Exam Strategy for Comparing Water Tariffs

The final paragraph addresses a common exam scenario where students are asked to compare the costs of different tariff levels. The script provides a step-by-step guide on how to calculate the charges for 19 kiloliters of water under both level one and level two tariffs. It demonstrates the process of breaking down the total usage into the relevant pricing tiers and calculating the cost for each tier. The difference in cost between the two tariff levels is then determined, highlighting the importance of careful calculation and understanding of tariff structures in exam situations. The video concludes with a suggestion for viewers to practice these calculations independently to reinforce their learning.

Keywords

💡Tariffs

Tariffs are a billing system used by service providers to determine how customers are charged for goods or services. In the context of the video, tariffs are the focus, particularly water tariffs, which are a complex section of tariffs that, if understood, can make other types of tariffs easier to grasp. The script uses the example of a cell phone provider charging per minute of talk time to illustrate the concept.

💡Water Tariffs

Water tariffs are a specific type of tariff that deals with the billing for water usage. The video script explains that understanding water tariffs is essential as they are often the most complex and can award the most marks in exams. The script provides an example of calculating water tariffs based on the amount of kiloliters used by a household.

💡Kiloliter

A kiloliter is a unit of volume equal to one thousand liters. In the video, water is charged per kiloliter, meaning for every thousand liters of water used, a household is billed accordingly. The script uses kiloliters as the unit for the example calculations of water tariffs.

💡Billing System

A billing system is the method or mechanism by which a service provider charges customers for the services they use. The video script describes various examples of billing systems, such as cell phone providers charging per minute of talk time or parking tariffs based on the duration of parking.

💡Service Provider

A service provider is a company or entity that offers services to customers. In the script, examples of service providers include cell phone companies like MTN and municipal services that provide water. The video discusses how these providers use tariffs to charge customers for the services they consume.

💡Calculations

Calculations in the context of the video refer to the mathematical process of determining the cost of water based on the amount used and the corresponding tariff rates. The script provides detailed steps on how to calculate the total cost for different amounts of water usage, using multiplication and addition.

💡Exam Situation

An exam situation is a hypothetical scenario presented in an exam or test. The video script includes an example of an exam question where a household's water usage is given, and the task is to calculate the cost difference between two different tariff levels. This demonstrates how the concept of tariffs can be applied in an academic setting.

💡Level One and Level Two Tariffs

The script introduces two levels of tariffs, Level One and Level Two, to illustrate the difference in cost for the same amount of water usage. Level One tariffs are described as cheaper, while Level Two tariffs are more expensive. The video uses these levels to show how to calculate the difference in cost for 19 kiloliters of water usage.

💡Municipality

A municipality refers to the local governing body that typically provides public services, including water supply. In the script, the municipality is the entity that charges households for water usage, and understanding their billing system is crucial for calculating water tariffs.

💡Price Ranges

Price ranges in the context of the video are the different tiers of water usage that have specific cost rates. For example, the first six kiloliters might have one price, and any usage beyond six kiloliters up to a certain amount might have a different, often higher, price. The script explains how to calculate the total cost based on these price ranges.

💡Rounding Off

Rounding off is the process of adjusting a number to the nearest whole number, typically for ease of calculation or reporting. The script mentions that decimals should be used in intermediate calculations but the final answer should be rounded off to the nearest cent for the total cost of water usage.

Highlights

Introduction to the channel dedicated to turning struggling math students into math masters.

Posting schedule for educational videos on Tuesdays and Thursdays.

Encouragement to subscribe and enable notifications for new content.

Focus on teaching tips and tricks for understanding tariffs, specifically water tariffs.

Explanation of the importance of mastering water tariffs due to their complexity and high marks potential.

Definition of a tariff as a billing system used by service providers.

Examples of tariff systems in different contexts such as mobile networks and parking.

Clarification on water tariffs being charged per kiloliter.

Understanding the concept of tiered pricing in water tariffs based on usage.

Demonstration of how to calculate charges for different levels of water usage.

Example calculations for households using 5, 8.3, and 13 kiloliters of water.

Explanation of how tiered pricing affects the cost of water usage.

Strategy to understand the pricing structure by calculating for smaller ranges first.

Illustration of how to calculate the total cost for a household using 13 kiloliters.

Advice on practicing with the provided example to solidify understanding.

Discussion on exam-type questions involving comparison between different tariff levels.

Step-by-step guide to calculate the difference in charges between level one and level two tariffs.

Encouragement for viewers to engage with the content by pausing, practicing, and asking questions.

Closing remarks with an invitation to the next video and a thank you for watching.

Transcripts

hey there smart monkeys welcome to my

channel and if you've been here before

welcome back

um so this is my little platform where I

turn struggling math students into maths

Masters okay I post videos Tuesdays and

Thursdays so be sure to subscribe and

turn on the notification Bell um Bell to

make sure that you get notified when I

actually post new videos okay so in this

video I want to be teaching you some

really nice tips and tricks on how to

approach

tariffs okay and specifically water

tariffs

um yeah so that's what we're going to

look at in this video and hopefully I

can make this a little bit easier for

you to understand okay so

let's do this

[Music]

okay so as I mentioned we are looking at

tariffs

um and in this video I'm gonna focus on

water tattoos because this is a section

on tariffs that usually is awarded the

most marks if they ask this question and

also it's the most complex so if you get

it if you understand how water tariffs

work then I'm pretty sure that all the

other types of tariffs would be easy for

you to understand

okay so before we start let's just make

sure we understand what a tariff

actually is right so a tariff is a

billing system used by a service

provider which determines how customers

and clients are charged for goods or

services

how what what is the system that they

use to actually charge their clients so

for example if you look at a a cell

phone provider or a network provider you

know MTN will charge you x amount per

minute that you talk on the phone or

they will charge you so much for

WhatsApp and for WhatsApp bundle if you

go to underground parking you'll see

that on the front day they would

literally be the Tariff system that they

use for parking there so usually it's

like for the first half an hour it's

free and then if you go there for an

hour you pay x amount you'll be there

for two hours you pay x amount

so that entire system

of how they plan to bowl you or to

charge you that's just called the Tariff

system so don't be overwhelmed by the

concept okay so that's what tariff means

and in this video we're going to focus

specifically on water tariffs and how

you are actually charged for water so a

few things that you need to understand

for this one when you you obviously are

paying the municipality for water right

and water is generally charged per

kiloliter okay so to give you sort of an

understanding kilolita is a thousand

liters so for every thousand liters that

your household uses you're going to be

charged

okay

so we're going to look at this example

and then I'm going to show you how you

actually do the calculations for this so

the example says

the theft used for water is given in the

table

use the table to calculate how much a

household would pay for using five

kiloliters 8.3 kiloliters and 13

kiloliters so we're looking at this as

if this household used this total for

the month okay so

if we look at this in the left hand side

of the table you will see that this is

the amount of kiloliters and on the

right is how much is charged per

kiloliter now the thing that I want you

to understand here Great Walls is

that

the more you use in this case the more

you'll be charged for what you use okay

so let's say somebody to somebody uses

six kiloliters then that means that

they're gonna follow six kiloliters

they're going to be charged 4 and 65 for

each kiloliter

so to calculate that total you would

then say the 4.65 multiplied by the 6.

right

but let's say this person used seven

kiloliters

the first six will always be charged at

the same amount

right so you're still going to say 6

multiplied by 4.65 but now the seventh

kiloliter will fall in this range which

means only one kiloliter will then be

charged at 17 and 75. so if you choose

to use more

then that means even though the first

six will then be charged as per usual as

per normal for everybody no matter how

much you use

and then as you go the more you use for

those kiloliters will be charged at a

higher expense so let's actually do the

calculations so that you know what I

mean

so the first person used five kiloliters

so if I look at my table here you see

five will obviously fall into this range

so if they use five kiloliters and it's

4 and 65 per kiloliter then the

calculation is simple then this per this

household for the month will then have

to pay 23 Rand 25 cents

that's fairly simple okay now let's look

at a family that uses 8.3 kiloliters

now what I want you to know and to note

as I mentioned before the first six

is still the same price right so the six

which is this range

times the the price for each is 27.90 so

this is the price for the first six

kiloliters that they used

after the six kiloliters you'll see that

there's still 2.3 kiloliters that we

need to be charged for this now falls in

the second interval range right so then

we'll go 2.3 multiplied by now the third

four four if you use more than six

is then

20 2.3 times 17.75 note usually this

will say more than six kiloliters

because I know people will ask oh but

man but if it's six kilo liters there's

a six there and there's a 60.

um in this case uh or in your exams I

will always say more than so then you

know that six will then fall in this

interval and then more than six will

fall in this interval

okay

so then to find out the total amount it

would then be the first six

plus the 2.3 and then together that will

be what this household will be charged

which is 68 Rand and 73 cents

okay

now let's have a look at 13 kilo liters

because now we're actually moving beyond

just our first two intervals so watch

this again the first six charged per use

per normal equals 27.90 see that's the

same as the first six

um for the household that used 8.3

then we have

the next 4.5

which is being charged at 17.5 how did I

get that 4.5 you just take this minus

that and it tells you how many

kiloliters actually is in this range

which is 4.5 and that's how much being

charged so the first six is charged at

this price is this total and in the next

4.5 is this total over yeah now if we

have a look we notice that we have only

now

calculator or being charged for 10.5

because remember look at this values

here

the first six and then the next 4.5 that

gives me ten and a half which means that

I still need to be charged the rest to

make up the 13 which is the 2.5 okay so

this total year on the left must always

add up to the actual amount of

kiloliters that the household has used

and the 2.5 Falls now in this range and

this is the price for it therefore that

will be how much they will be charged

for that 2.5

so in total this family is going to be

charged the following for the first six

27 and 90 for the next 4.5 they used

it's

79.875 remember always use all the

decimals you only round off your final

answer

and then at the end you the last 2.5 was

then a little bit more expensive and it

cost them 64 Grand point nine to five so

in total this household that used 13

kiloliters will then be charged at 172

Rand and 70 cents

okay so the secret here is understanding

that the earlier

um water the smaller amounts that it's

used obviously the less you pay but this

the smaller range will always be how

much you are going to be charged

regardless

of what the big total is So the first

six will always be 27 and 90 whether

this family used a hundred kiloliters or

whether this family used only six that

first six will always be the same price

okay so I hope this sort of clarifies

that a little bit for you now let's look

at how can they ask this in an exam type

situation okay so let's read carefully

yeah so this question says water was

bold at a level two tariff in November

2022.

for a household in Cape Town if this

home used 19 kiloliters determine how

much more they paid for level two than

if they were bold at level one

all prices include that

so if we have a look here they say that

this household was charged by level two

um tariffs okay so level one tariff

is basically uh sort of the cheaper

tariff and then level two is the more

expensive data but now what they want to

know is how much more is this family

going to be charged if they get charged

level two versus if they were going to

be charged with level one

so you see the same concept

but now the type of question that's

being asked here

right means that you actually have to

calculate

19 kiloliters for both level 1 and level

two and to find out how much more you

would then calculate the difference

between those two answers okay so let's

do that let's start off with level one

so this person between 0 and 6

if it was level one the first six would

then be 3 and 75 that would then be the

total then the next

4.5 is then charged at 13.75

and then so this is already 10.5

remember we we use this household use 19

kilo kiloliters so we have to continue

up until we get to 90.

then the next one is

whatever the difference is here so the

what is the range of kiloliters year

it's 8.5 right so 20 minus the 10.5 will

give you the 8.5 right so in this range

the 8.5 which was used will be charged

at 24.96

right and then how much do we have then

in total right we then have sorry we

didn't have

six

plus the 4.5 gives us the 10.5 right

plus the 8.5

this total then gives us the 19.

okay

and so the first six was charged at that

amount the next 4.5 was charged at this

amount and the next 8.5 was then charge

at this value

which means the total so do you notice

that more than 20 this tariff is not

going to be relevant to our question

because we're only working with 19

kiloliters so then our total then would

be the first six the next 4.5 and then

the next 8.5

okay which will give you 296.535

then

we do the exact same but we're now going

to be using third level two tariffs so

again it's the six but now it's charged

it's a bit more expensive then the next

4.5 will be charged at 32.45

then the next one

um 8.5 will be charged at 84 Rand and

then the total will then be the 53 which

is the first six the next 4.5 and the

next 8.5 which gives us a total of 19

will then be will then cost

913.605 note I didn't round off any of

these answers yet because it's not my

final answer

excuse me so to get to the final answer

which is what they're asking what is the

difference between the two I just take

that answer

and I subtract that one so this person

this household would then have be paying

617 Rand and seven cents more

uh being charged at level two tariffs

versus at level one status

okay what I want to suggest to you is

go back

to the video and pause it with just the

question and the table is shown

and then you try without

um looking at the answers that I've

given and you try and see if you get to

the same answers that I get because

watching this is very easy because I'm

busy doing it but when you actually do

it yourself that's when you actually

learn so now that you've seen this

explanation I want you to pause the

video then go back to where this video

where I show just the example without

the answer and you try and see if you

can work out through the steps that I've

shown you now to actually get to the

correct answer

okay so yeah thank you so much and yeah

good luck I hope this this video really

helped you understand tariffs a bit

better

so did that video help you at all I hope

it did

um yeah if you liked it please give it a

thumbs up and if you have any questions

you know what to do

um so yeah thank you so much for

watching and I'll see you in the next

video bye