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Ratios & Proportions Chapter 3 McGraw-Hill Ryerson©

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**Learning Objectives also… Set up and solve proportions**

Ratios Proportions 3 Learning Objectives After completing this chapter, you will be able to: LO 1. Set up and manipulate ratios LO 2. & 3. Set up and solve proportions Use proportions to allocate or prorate an amount on a proportionate basis also…

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**Use quoted exchange rates to convert between currencies**

Learning Objectives LO 4. Use quoted exchange rates to convert between currencies Relate currency exchange rate movement to currency appreciation or depreciation LO 5.

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**Expressing a Ratio in Equivalent Forms**

Ratios Proportions 3 LO 1. Mcgraw-Hill Ryerson©

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**Expressing a Ratio in Equivalent Forms Q**

LO 1. Q Colleen, Heather and Mark’s partnership interests in Creative Crafts are in the ratio of their capital contributions of $7800, $5200 and $6500 respectively. What is the ratio of Colleen’s to Heather’s to Marks’s partnership interest?

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**Expressed In colon notation format**

Expressing a Ratio in Equivalent Forms Colleen, Heather and Mark’s partnership interests in Creative Crafts are in the ratio of their capital contributions of $7800, $5200 and $6500 respectively. Colleen Heather Mark Expressed In colon notation format 7800 : 5200 : 6500 Equivalent ratio (each term divided by 100) : : 78 52 65 Equivalent ratio with lowest terms Divide 52 into each one : :

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**Expressing a Ratio in Equivalent Forms Q**

The ratio of the sales of Product X to the sales of Product Y is 4:3. The sales of product X in the next month are forecast to be $1800. What will be the sales of product Y if the sales of the two products maintain the same ratio?

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**Divide both sides of the equation by 4**

Expressing a Ratio in Equivalent Forms The ratio of the sales of Product X to the sales of Product Y is 4:3. The sales of product X in the next month are forecast to be $1800. Since X : Y = 4 : 3, then $1800 : Y = 4 : 3 $1800 4 = Cross - multiply Y 3 Divide both sides of the equation by 4 4Y = 1800 * 3 Y = 1800 * 3 = $1350 4

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**Expressing a Ratio in Equivalent Forms Q**

A 560 bed hospital operates with registered nurses and other support staff The hospital is about to open a new 86-bed wing. Assuming comparable staffing levels, how many more nurses and support staff will need to be hired?

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**S Expressing a Ratio in Equivalent Forms**

A 560 bed hospital operates with registered nurses and 185 other support staff The hospital is about to open a new 86-bed wing. 560 : 232 : 185 = 86 : RN : SS S R N 560 86 560 86 Hire or RN’s = Hire or SS = 185 232 RN SS 560RN = 232*86 560SS = 185*86 560RN = 19952 560SS = 15910 RN = / 560 SS = / 560

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**Expressing a Ratio in Equivalent Forms Q**

LO 2. & 3. Q A punch recipe calls for fruit juice, ginger ale and vodka in the ratio of 3:2:1. If you are looking to make litres of punch for a party, how much of each ingredient is needed?

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*** 3 * 2 * 1 Expressing a Ratio in Equivalent Forms 3+2+1 = 6**

A punch recipe calls for fruit juice, ginger ale and vodka in the ratio of 3:2:1. F J G A V Total Shares 3+2+1 = 6 333 ml per share 2 litres / = 333 ml per share * 3 * 2 * 1 = 1 litre = 667 mls = 333 mls

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**If you have 1.14 litres of vodka, how much punch can you make?**

Expressing a Ratio in Equivalent Forms Q A punch recipe calls for fruit juice, ginger ale and vodka in the ratio of 3:2:1. If you have 1.14 litres of vodka, how much punch can you make? 3+2+1 = 6 Total Shares 1 1.14 = Cross - multiply 6 Punch Punch = 6 * 1.14 litres = 6.84 litres

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**Expressing a Ratio in Equivalent Forms Q**

You check the liquor cabinet and determine that someone has been drinking the vodka You have less than half a bottle, about 500 ml. How much fruit juice and ginger ale do you use if you want to make more punch using the following new punch recipe? Fruit juice: ginger ale: vodka = 3 : 2 : 1.5

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**Expressing a Ratio in Equivalent Forms**

How much fruit juice and ginger ale do you use if you want to make more punch using the following new punch recipe?: Fruit juice: ginger ale: vodka = 3 : 2 : 1.5 500 ml F J G A 3 F J 2 G A = = Cross - multiply Cross - multiply 1.5 0.5 1.5 0.5 Fruit Juice = 3 * 0.5 /1.5 Ginger Ale = 2 * 0.5 /1.5 = 1 litre = .667 litre = 667 ml.

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Percent Change %

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**Percent % Change Q If $1000 grows to $2500, find the percent change**

Initial Value Final Value % (/100) Difference or Change $ 1000 100 1 2500 250 2.5 1500 150 1.5 If $1000…………= 100% or 1 What does $2500 = ? = 100% x 2500 Cross - multiply 1000 X = 2500*100% / 1000 = % …Also

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**This method is referred to as**

Percent Change % Q If $1000 grows to $2500, find the percent change We can use the following alternative method to calculate the percent change! Review Chapter 1 Initial(Base)Value Final Value Difference $ 1000 This method is referred to as the Base Method 2500 $ 1500 $1500 % change = $1000 % change = Difference Base = or 150% increase

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Percent Change % Q If 15kg. of fruit shrinks to 3 kg. in the drying process, find the percent change. Initial Value Final Value % (/100) Difference or Change Kg. 15 100 1 3 20 .2 12 80 .8 If 15kg.…………= 100% or 1 What does 3kg. = ? = 100% x 15 3 Cross - multiply X = 3*100% / 15 = 20%

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**Converting Percent Differences to Proportions**

Change % Converting Percent Differences to Proportions Two companies, Markham Tire and Unionville Tire, normally offer the same tire prices. Markham Tire has now marked-down the price of its Bridgestone Blizzard tires by 20%. What percentage more will you pay if you buy your new tires from Unionville Tire? Be Aware

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**Percent % Change Example A: Example B: Example C: AND... Be Aware = =**

…when interpreting certain comparisons! “A is 40% of B” Example A: A B = 40 100 Means … A = 40 when B = 100 and “A is 40% greater than B” or “A is 140% of B” Example B: Mean … A = = 140 when B = 100 and A B = 140 100 “A is 40% less than B” or “A is 60% of B” Example C: … A = when B = 100 and A B = 60 100 Means AND...

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**Percent Change % Limits**

Be Aware If A and B both represent positive quantities, it is NOT POSSIBLE that “A is 140% Less than B” Limits The limit is “A is 100% less than B” …which makes A = 0 Back to the tire question

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**Percent Change % = = = 1.25 or 125% …both MT & UT = 100%**

Two companies, Markham Tire and Unionville Tire, normally offer the same tire prices. Markham Tire has now marked-down the price of its Bridgestone Blizzard tires by 20%. What percentage more will you pay if you buy your new tires from Unionville Tire? MT = 100 – 20 = 80 MT UT = 80 100 To find the ‘price size’ of UT compared with MT, we invert the proportion… UT MT = 100 80 = 1.25 or 125% UT charges 125% of MT’s price(25% more than MT)

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C urrency Europe North & South America Asia Africa Australia E xchange

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**C urrency E xchange Points**

LO 4. As we just saw, every area in the world uses some form of currency The currency of one country may not be able to be converted into that of another on a one-for-one basis. …some are recognized as having more value than others. Points In order to place each currency on an ‘equivalent basis’, it is necessary to ‘exchange currency’ at the prevailing rate in the marketplace.

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**Some major ‘marketplaces’ for prevailing currency rates**

Frankfurt

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**Table 3.1 Foreign Exchange Rates (noon, Toronto, April 11, 2001)**

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**Table 3.2 Currency Cross rates (noon, Toronto, April 11, 2001)**

US$ Euro DM F S Canadian $ = C Y

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**y C urrency E xchange Q = ¥39,910 ¥ y ¥ * C$500 C$ Y ¥79.82 =**

Using the exchange rates given, calculate the number of yen that C$500 could purchase. Canadian $ C$ If a C$.…………… = What does C$ = ? Y = ¥79.82 y = Cross - multiply C$500 C$1 = ¥39,910 Purchase y ¥79.82 * C$500 = C$1.00 Note

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**C urrency E xchange C C$ 1 Y … instead of this,**

we could use the following exchange rate to find the number of Canadian$’s that each yen will buy! Canadian $ C$ US$ Euro DM Y = C C$ 1 Y = = Calculation

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**y C urrency E xchange Q = ¥39,910 ¥ y ¥ * C$500 ¥1 ¥1 Cross - multiply**

Using the exchange rates given, calculate the number of yen that C$500 could purchase. If C$ … = What does C$ = ? ¥1 y C$500 ¥1 Cross - multiply = C$ = ¥39,910 Purchase y C$ ¥1 * C$500 =

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**C urrency E xchange Q = C = = Y = C$100.22**

Using the exchange rates given, calculate the number of Canadian$ that could buy. Y = Q Canadian $ C$ US$ Euro DM Y = C C$ If a ……………… …. = C$ What does = ? C$ C$X ¥1.00 = Cross - multiply ¥8000 = Purchase C$100.22 C$ = * ¥8000 ¥1.00

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**C urrency E xchange Q Step Step**

How much will it cost in Canadian dollars to purchase US$500 of currency at a bank that charges % commission on the transaction? Assume C$ = US$1.00 Step Calculate the cost of US$ in Can$ Step Calculate the commission cost in Can$

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**C urrency E xchange Step * 1.5% = Step C$1.5628 C$ ? C$781.40 US$1.00**

How much will it cost in Canadian dollars to purchase US$500 of currency at a bank that charges 1.5% commission on the transaction? Assume C$ = US$1.00 C$ cost to Purchase US$500 Step C$1.5628 C$ ? C$781.40 US$1.00 = C$793.12 US$500 Commission Step * 1.5% = C$781.40 C$11.72

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**(1 US gallon = 3.785 litres) Assume C$1.5628 = US$1.00**

xchange C urrency Q Gasoline sold for C$0.659 per litre in Vancouver and US$1.39 per gallon in Seattle. How much cheaper (based on the Vancouver price) was gas in Seattle? (1 US gallon = litres) Assume C$ = US$1.00 Step Calculate the cost in Canadian$ for the equivalent of 1 gallon of gas. Step Convert US$1.39 to C$. Step How much cheaper is the gas in Seattle?

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**C urrency E xchange Step Step Step * US$1.39 = C$0.322 cheaper**

Gasoline sold for C$0.659 per litre in Vancouver and US$1.39 per gallon in Seattle. How much cheaper (based on the Vancouver price) was gas in Seattle? (1 US gallon = litres) Assume C$ = US$1.00 Step 3.785 litres C$0.659 per litre = C$2.494 Step C$X C$1.5628 = Cross - multiply US$1.39 US$1.00 C$1.5628 C$X = * US$1.39 = C$2.172 US$1.00 Step C$ = C$0.322 cheaper C$2.172

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**If C$ drops 0.5%, we can buy .995(DM 1.4104)**

xchange C urrency LO 5. Q If the C$ weakens by 0.5% relative to the DM, what will be the new values for DM per C$1.00 and C$ per DM1.00? Canadian $ C$ C$1.00 = DM1.4104 If the Canadian dollar weakens, that means that we can buy fewer DM with each dollar! If C$ drops 0.5%, we can buy .995(DM ) or DM C$1.00 = DM Values New 1 = C$0.7125 DM1 = DM

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**This completes Chapter 3**

Mcgraw-Hill Ryerson©

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