Transcript A. Proportional Money

Math 10: A and W
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Find the definition of
each of the following
terms:
Buying Rate
Exchange Rate
Mark up
Promotion
Proportion
Rate
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Ratio
Selling Rate
Unit Rate
Unit Price
Percent
Currency
Discount
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Math on the Job p.12
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Read through together and solve
a) Ratio – remember that a ratio compares 2
numbers that are measured in the same units
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It can be written in several ways:
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Examples
20 𝑡𝑜 50,
20: 50
,
20
50
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20
50
The notation will be lost useful to us
because our knowledge of fractions can help
us to solve equations
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When working with ratios its always best to
simplify first.
Example
Simplify
20
50
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The two ratios 20:50 and 2:5 are equivalent
20
2
statements and the fractional equation = is
50
5
referred to as a Proportion
Ratios are expressed in real-life situations as
proportions.
For example, you may need to mix a certain
shade of paint. The proportion needed is 3 parts
blue and 1 part blue, or 3:1. You can use the
ratio to mix the amount of paint you need in the
correct proportion.
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In a ratio, since the units are the same, they
essentially cancel each other out.
So when doing calculations you can omit the
units but must remember to included them in
your answer.
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Discuss the Ideas – Adapt a Recipe p. 13
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Read through together and solve
1. Engines that require you to mix oil with fuel
to provide lubrication area called 2-stroke
engines. A faller as a logging site needs to
refill a chainsaw’s fuel can. The ratio of
gasoline to oil that is needed is 40 parts of gas
to one part if oil. The chainsaw’s fuel tank can
hold 8 liters of gas. How mush oil should be
added to the gasoline to obtain the correct
ratio?
2. Josh, a builder, has found that he can
arrange the work cubicles of his employees
best if the ratio between the length and the
width if a room is 3:2. If a room is 6m long,
how wide should the room be?
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Activity 1.1 – Visualize a Proportion p.15
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Work through individually using graph paper
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Activity 1.2 – Fruit Drink Taste Tester p.16
Work through individually making a copy of
the chart in your notes
b) Rate – is a similar ratio, but it compares 2
numbers with different units
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Examples
Number of words per minute
Price of lumber per foot
Price of apples per pound
Speed in kilometers per hour
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A rate can be expressed in the same way as a
ratio.
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Because the units are different they must be
included.
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For example if you see salmon on sale for
$1.89 for 100 grams you can write it as:
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$1.89:100 grams, $1.89/100 grams, or
$1.89
100𝑔
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You can also think of a proportion as an
equivalent statement between 2 rates.
For example, lets write a proportion for the
salmon sale rate we just looked at.
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Discuss the Ideas – Speed Skater p. 18
Read through together and solve
1.
2.
If salmon costs $1.89 for 100 grams, how
much will it cost to but 250g of salmon?
A local plumber store sells 100 copperplated pipe straps for $4.97. You have
estimated that you require 75 straps. How
much will you pay for 75 straps?
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No calculators allowed, try to just use your
brain.
1. The pipe straps in the previous example
each cost $0.0497. About how much will 50
straps cost?
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Ex. 1.1 (p.21) #1-9
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Math on the Job p. 23
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Read through together and solve
a) Unit Price
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Different brands may package their products
in different sizes of packages
Finding a unit price will allow you to compare
prices, and help you determine the best buy
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Consumer goods, such as pens and toilet
paper are sold in bundles. To compare the
price when the quantity in the package is not
the same, it is often useful to look at the unit
cost of one item.
Businesses who purchase in bulk and then
want to charge customers for one item at a
time also need to calculate the cost of 1 item
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A Unit Price is the cost of one unit. It is
sometimes referred to as a unit rate.
To calculate a unit price, you can set up a
proportion when the second rate has a
denominator of 1
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If you buy a package of 4 rolls of paper towel
for $2.68, calculate the cost of one roll.
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Therefore, cost per unit or unit price can be
determined by dividing the price of a product
by the number of units contained in a
product
$ 𝑐𝑜𝑠𝑡
= 𝑢𝑛𝑖𝑡 𝑝𝑟𝑖𝑐𝑒
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑛𝑖𝑡𝑠
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Comparing unit prices can save you money at
home and in the workplace
What other factors should you consider when
purchasing items in packages:
More than you need
Previous experience with brand
Quality of product
1.
Steph buys supplies for the hamlet office in
Arviat, Nunavut where she works as a clerk.
She wants to buy pens. The supplier sells a
box of 12 pens for $6.25. Calculate the
unit price of 1 pen.
2.
Bryce picks fresh strawberries at a U-pick
farm in Portage la Prairie, Manitoba. If he
fills a pint basket (0.5506 liters), it will cost
him $1.50. If he fills a 4-liter ice cream
pail, it will cost $9.00. Which size of
container will give her a better buy?
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Activity 1.3 – Which Price is Right? P. 25
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Work through with a partner.
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Ex. 1.2 (p.26) #1-7
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Math on the Job p. 28
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Why would businesses have sales?
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Read through together and solve
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What must be taken into consideration when
estimating a job and what are consequences
that happen when it is done poorly?
Estimating to little time can lead to labour
shortages, costs over running, disappointed
clients and so on. The cost estimator must
ensure that the final price covers all cost plus
make a profit.
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Prices rise and fall due to consumer demand
and supply.
If demand rises, suppliers are able to charge
more.
If demand falls, or if there is a large supply of
a product, prices may fall.
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Prices also rise and fall according to the cost
of the materials and labour that go into the
creation of a product or services
An additional amount, called Markup, is
added to these costs so that a profit can be
made.
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For example, when an owner of a market
buys items to re-sell them, he or she buys
them at a wholesale price. They then markup
that price so the item is sold at a higher price
to make a profit.
The markup, is usually a percent of the
wholesale price
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When setting a price for goods and services,
companies consider psychological factors
that have an impact on buyers as well.
Have you ever wondered why something
costs $39.95 instead of $40.00?
The final price is not that different but it seems
less expensive to the buyer before taxes.
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A butcher may advertise a price of
$2.39/100g for meat instead of $23.90/kg
because it seems less expensive, even though
they are equivalent.
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Remember that in many cases taxes are added to
arrive at the total price. Taxes are calculated as a
% of the price paid.
All Canadians pay the Federal Goods and Services
Tax (GST), which is 5%. Most Provinces also
charge a Provincial sales tax (PST)
Alberta 0%
BC 7%
Manitoba 7%
Saskatchewan 5%
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Discuss the Ideas – Concert Promoter p.29
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Read through together and solve
1.
Mackenzie purchases fabric at a wholesale
price for her custom sewing business in
Dawson City, YT. She pays $46.00/m. She
charges a markup of 20% on the fabric.
What will Mackenzie charge her clients per
meter?
2. A furniture store in Saskatoon is selling a
bedroom suite. The list price for the suite is
$1599.00. What will the total cost be,
including GST and PST?
1. If you set the price of a bike helmet at
$49.95 and sell 25, how much less income will
your store generate than if you sold the same
number at $54.95?
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Ex. 1.3 (p.22) #1-8
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Math on the Job p. 34
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Read through together and solve
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Often when you are shopping you may see
something on sale for a discount price. The
discount is usually expressed as a %.
For example, 20% or 50% off
Businesses may use other sales promotions
to attract buyers. Companies usually give a
certain amount off the retail price, $25 or
$1.00 for example
a) Percent Increase and Decrease
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 − 𝑛𝑒𝑤 𝑝𝑟𝑖𝑐𝑒
% Decrease=
× 100
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒
𝑛𝑒𝑤 𝑝𝑟𝑖𝑐𝑒 − 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒
% Increase=
× 100
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒
1.
2.
Al Anderson’s Source for sports has marked
down its one piece hockey sticks from
$280.00 to $200.00. What is the %
decrease?
A ticket scalper is trying to sell tickets to an
AC/DC concert. He bought the tickets for
$150 a piece and is selling them for $400 a
piece. What is the % increase per ticket?
3.
Justin needs to buy a new winter jacket. He
has waited for a sale, and a jacket that
originally cost $249.95 is now discounted
20%. How much will the jacket cost if Justin
lives in Nunavut, where there is no PST?
4.
A fisher sells fresh salmon, live crabs, and
prawns at the dock in Steveston, BC directly
to customers on Saturdays and Sundays. As
the weekend winds down, he needs to sell
off his stock, otherwise it will spoil. He has
a sale! He offers 20% off all his prices.
Salmon is regularly $18.50/kg and prawns
are $34.50/kg. At a 20% discount, what is the
price of a salmon what weighs 3kg? How much
would 500g of prawns cost?
1. You are shopping at a sale and see a
$995.00 bbq marked down 20%.
Approximately what price do you estimate the
sale price is before taxes?
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Activity 1.4 – Taking Advantage of Sales
Promotions p. 36
You may work in partners
Make a copy of the table in your book and fill
it in and answer the questions that follow
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Ex. 1.4 (p.37) #1-7
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Math on the Job p. 41
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Read through together and discuss solutions
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What are items you have at home that are not
usually from Canada?
Electronics, vehicles, clothes
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Because many of the items we use come from
different countries the company that
purchases must convert Canadian dollars to
the international currency of the country
when the product is produced
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What products does Canada export?
lumber, wheat, buses, etc
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Again a seller must convert the amount
received from the buyer to Canadian funds.
Sellers must also price the product to
minimize loses from the fluctuating dollar
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How will the rise and fall of the Canadian dollar
affect the import and export of goods?
High dollar:
More import because we don’t have to pay as
much
Less exports because other countries have to pay
more
Low Dollar:
More exports because other countries don’t have
to pay as much
Less imports because it costs more for products
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Since people travel to different countries,
businesses trade with different countries and
different countries use different currencies,
international trade requires an organized
system for exchanging money.
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Banks, currency exchange companies and
travel agencies can all exchange currencies.
Not all currencies are available when ever you
might want them so it is important to plan
ahead.
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If a Canadian company wants to buy goods
made in Japan, it must exchange Canadian
dollars for yen to complete the purchase
The exchange rate between the 2 countries is
used to calculate how many dollars the
company must convert
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Exchangers set a selling rate and a buying
rate for currency exchange and are different
from each other. Both are from the
perspective of the bank.
If you want euros from the bank you are
using the selling rate and if you are returning
from Europe and want Canadian dollars back
you are using the buying rate.
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You pay more for foreign currency than the
banking institution will pay in return.
When travelling in a foreign country, it is
often helpful to estimate what something
costs in your own currency to compare prices
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If the exchange rate for the euro is
$1.644814 CAD and your hotel in Paris cost
€95.00, about how much is your hotel in
Canadian dollars?
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The value of a nations currency, and thus its
exchange rate compared to other currencies
is influenced by many factors, from the
general (a countries economic and political
status) to the specific (interest and
employment rates).
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When buying and selling money from the
bank in an exchange rate you will always lose
money.
The bank will always sell you the money at a
higher rate then they will buying it back from
you. (look at table on p. 45)
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To solve exchange rate problems we set up a
proportion
One side of the proportion has the exchange
rate and the other side has the money we
want to be converted
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Proportional Statement for Currency Exchange:
1 𝑓𝑜𝑟𝑖𝑒𝑔𝑛 𝑑𝑜𝑙𝑙𝑎𝑟
𝑓𝑜𝑟𝑖𝑒𝑔𝑛 𝑐𝑜𝑣𝑒𝑟𝑡𝑒𝑑 𝑎𝑚𝑜𝑢𝑛𝑡
=
𝐶𝑎𝑛𝑎𝑑𝑖𝑎𝑛 𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝐶𝑎𝑛𝑎𝑑𝑖𝑎𝑛 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑑 𝑎𝑚𝑜𝑢𝑛𝑡
1.
2.
On a specific date, the selling rate for the
Danish krone compared to the dollar is
0.221778. How many kroner will you
receive for $500 Canadian?
On the same day as #1 occurs, the buying
rate for kroner was 0.210778. If, after
purchasing your kroner, you decided not to
go to Denmark and sold the kroner back to
the bank, how did you lose?
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Activity 1.5 – What’s your ride? p. 42
We will not use the internet we will just use
our chart on pg. 45 to fill in the chart the you
will copy into your text book
Then select a car that you would have bought
and change that money order that you would
have needed back to Canadian dollars and
find the amount of money you will lose on the
transaction.
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Ex. 1.5 (p. 47) #1-7