A. Proportional Money

Math 10: A and W

Key Terms: Find the definition of

each of the following terms:

Buying Rate Exchange Rate Mark up Promotion Proportion Rate

Ratio Selling Rate Unit Rate Unit Price Percent Currency Discount

Math on the Job p.12

Read through together and solve

1. Proportional Reasoning

a) Ratio – remember that a ratio compares 2 numbers that are measured in the same units

It can be written in several ways:

Examples

The notation will be lost useful to us because our knowledge of fractions can help us to solve equations

When working with ratios its always best to simplify first.

Example

Simplify

The two ratios 20:50 and 2:5 are equivalent statements and the fractional equation is 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.

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.

Discuss the Ideas – Adapt a Recipe p. 13

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?

Example

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?

Example

Activity 1.1 – Visualize a Proportion p.15

Work through individually using graph paper

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

Examples

Number of words per minute Price of lumber per foot Price of apples per pound Speed in kilometers per hour

A rate can be expressed in the same way as a ratio.

Because the units are different they must be included.

For example if you see salmon on sale for $1.89 for 100 grams you can write it as:

$1.89:100 grams, $1.89/100 grams, or

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.

Discuss the Ideas – Speed Skater p. 18

Read through together and solve

1. If salmon costs $1.89 for 100 grams, how much will it cost to but 250g of salmon?

2. A local plumber store sells 100 copper-plated pipe straps for $4.97. You have estimated that you require 75 straps. How much will you pay for 75 straps?

Example

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?

Mental Example

Ex. 1.1 (p.21) #1-9

Building your Skills

Math on the Job p. 23

Read through together and solve

2. Unit Price

a) Unit Price

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

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

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

If you buy a package of 4 rolls of paper towel for $2.68, calculate the cost of one roll.

Example

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

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.

Example

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?

Example

Activity 1.3 – Which Price is Right? P. 25

Work through with a partner.

Ex. 1.2 (p.26) #1-7

Building your Skills

Math on the Job p. 28

Why would businesses have sales?

Read through together and solve

3. How Prices are Set

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.

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.

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.

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

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.

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.

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%

Discuss the Ideas – Concert Promoter p.29

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?

Example

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?

Example

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?

Mental Example

Ex. 1.3 (p.22) #1-8

Building your Skills

Math on the Job p. 34

Read through together and solve

4. Sales

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

1. Al Anderson’s Source for sports has marked down its one piece hockey sticks from $280.00 to $200.00. What is the % decrease?

2. 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?

Example

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?

Example

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?

Example

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?

Mental Example

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

Ex. 1.4 (p.37) #1-7

Building your Skills

Math on the Job p. 41

Read through together and discuss solutions

5. Exchanging Currency

What are items you have at home that are not usually from Canada?

Electronics, vehicles, clothes

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

What products does Canada export?

lumber, wheat, buses, etc

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

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

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.

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.

*

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

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.

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

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?

Mental Example

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).

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)

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

Proportional Statement for Currency Exchange:

1. 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?

2. 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?

Example

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.

Ex. 1.5 (p. 47) #1-7

Building your Skills