Grade 12 Mathematical Literacy: Tariffs
Summary
TLDRThis 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
- đ The channel's focus is on helping struggling math students become proficient in mathematics.
- đ New videos are posted on Tuesdays and Thursdays, with an emphasis on subscribing and turning on notifications for updates.
- đ§ The video specifically addresses water tariffs, a complex section of tariffs that often carries significant marks in exams.
- đą A tariff is a billing system used by service providers to determine how customers are charged for goods or services.
- đ Water tariffs are charged per kiloliter, with a kiloliter being equivalent to a thousand liters.
- đ The cost of water increases with usage, with different rates for different ranges of kiloliters used.
- 𧟠The video provides a step-by-step guide on how to calculate water tariffs using a given table.
- đ Examples are given to illustrate the calculation process for households using different amounts of water.
- đ The first six kiloliters of water are charged at a standard rate, regardless of the total amount used.
- đ The video explains how to calculate the difference in charges between two different tariff levels for a given water usage.
- đ 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
đ 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.
đ§ 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.
đ 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.
Mindmap
Keywords
đĄTariffs
đĄWater Tariffs
đĄKiloliter
đĄBilling System
đĄService Provider
đĄCalculations
đĄExam Situation
đĄLevel One and Level Two Tariffs
đĄMunicipality
đĄPrice Ranges
đĄRounding Off
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
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