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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -1 McGraw-Hill Ryerson©

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

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -3 Use quoted exchange rates to convert between currencies Relate currency exchange rate movement to currency appreciation or depreciation Learning Objectives LO 4. LO 5.

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -4 Mcgraw-Hill Ryerson© LO 1. Ratios Proportions Ratios Proportions 3 3

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -5 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? LO 1.

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -6 Colleen, Heather and Mark’s partnership interests in Creative Crafts are in the ratio of their capital contributions of $7800, $5200 and $6500 respectively : 6500 : ColleenHeatherMark Expressed In colon notation format Equivalent ratio (each term divided by 100) :: Equivalent ratio with lowest terms Divide 52 into each one 1.5 : 1 : 1.25

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -7 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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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -8 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 Y = 3 4 Cross - multiply 4Y = 1800 * 3 Y = 1800 * 3 4 Divide both sides of the equation by 4 = $1350

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -9 A 560 bed hospital operates with 232 registered nurses and 185 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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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© A 560 bed hospital operates with 232 registered nurses and 185 other support staff. The hospital is about to open a new 86-bed wing. 560 : 232 : 185 = 86 : RN : SS 560 = RN 560RN = 232*86 560RN = RN = / 560 Hire or 36 RN’s 560 = SS 560SS = 185*86 560SS = SS = / 560 Hire or 29 SS S S

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

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© A punch recipe calls for fruit juice, ginger ale and vodka in the ratio of 3:2: = 6 Total Shares 2 litres / 6 = 333 ml per share F JG AV * 3 * 2 * 1 = 1 litre = 667 mls = 333 mls 333 ml per share

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 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? = 6 Total Shares Punch 6 = Cross - multiply Punch = 6 * 1.14 litres = 6.84 litres

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 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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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 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 F JG A 1.5 = 3 F J ml Cross - multiply Fruit Juice = 3 * 0.5 /1.5 = 1 litre = G A 0.5 Ginger Ale = 2 * 0.5 /1.5 =.667 litre = 667 ml. Cross - multiply

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -16

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© If $1000 grows to $2500, find the percent change = 100% x 2500 X = 2500*100% / 1000 = 250% Cross - multiply If $1000…………= 100% or 1 What does $2500 = ? If $1000…………= 100% or 1 What does $2500 = ? …Also 250 Initial Value Final Value % ( / 100) Difference or Change $

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© We can use the following alternative method to calculate the percent change! If $1000 grows to $2500, find the percent change % change = Difference Base This method is referred to as the Base Method This method is referred to as the Base Method $ $ 1500 % change = $1500 = 1.5 or 150% increase Initial(Base)Value Final Value Difference

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© If 15kg. of fruit shrinks to 3 kg. in the drying process, find the percent change If 15kg.…………= 100% or 1 What does 3kg. = ? If 15kg.…………= 100% or 1 What does 3kg. = ? X = 3*100% / 15 = 20% Cross - multiply Initial Value Final Value % ( / 100) Difference or Change Kg. = 100% x 15 3

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© C onverting P ercent D ifferences to P roportions 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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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© Be Aware …when interpreting certain comparisons! “A is 40% of B” Means … A = 40 when B = 100 and ABAB = “A is 40% greater than B” or “A is 140% of B” Mean… A = = 140 when B = 100 and ABAB = “A is 40% less than B” Means … A = when B = 100 and ABAB = or “A is 60% of B”

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© Be Aware If A and B both represent positive quantities, it is NOT POSSIBLE that “A is 140% Less than B” The limit is “A is 100% less than B” …which makes A = 0 Back to the tire question

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 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? 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? …both MT & UT = 100% MT = 100 – 20 = 80 MT UT = To find the ‘price size’ of UT compared with MT, we invert the proportion… UT MT = = 1.25 or 125% UT charges 125% of MT’s price(25% more than MT)

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© Afric a North & South Americ a Europe Asia Australia

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© As we just saw, every area in the world uses some form of currency 1.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. 1.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. 2. In order to place each currency on an ‘equivalent basis’, it is necessary to ‘exchange currency’ at the prevailing rate in the marketplace. LO 4.

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© Frankfurt Some major ‘marketplaces’ for prevailing currency rates

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 3 -27

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© Table 3.1 Foreign Exchange Rates (noon, Toronto, April 11, 2001)

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© C$C$ US$ Euro DM FS Canadian $ = Y Table 3.2 Currency Cross rates (noon, Toronto, April 11, 2001)

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© Using the exchange rates given, calculate the number of yen that C$500 could purchase. * C$500 C$1.00 ¥79.82 = ¥y =Cross - multiply C$500 ¥79.82 C$1C$1 ¥ y = ¥39,910 Purchase Canadian $ C$C$ Note If a C$.…………… = What does C$500 = ? If a C$.…………… = What does C$500 = ? Y =

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© C$C$ US$ Euro DM Y = = … instead of this, Canadian $ C$C$ we could use the following exchange rate to find the number of Canadian$’s that each yen will buy! Calculation 1 Y = =

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© Using the exchange rates given, calculate the number of yen that C$500 could purchase. * C$500 C$ ¥1 = = Cross - multiply ¥y C$500 ¥ y = ¥39,910 Purchase If C$ … = What does C$500 = ? If C$ … = What does C$500 = ? ¥1 C$ ¥1

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© Using the exchange rates given, calculate the number of Canadian$ that 8000 could buy. Y = US$ Euro DM Y = = Canadian $ C$C$ Cross - multiply = Purchase C$ ¥8000 ¥1.00 = C$ C$X * ¥8000 ¥1.00 C$ = If a ……………… …. = C$ What does 8000 = ? If a ……………… …. = C$ What does 8000 = ? ¥ ¥

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 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$1.00 Calculate the cost of US$ in Can$ Calculate the commission cost in Can$

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© C$ US$500 C$ 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$1.00 C$ * 1.5% = C$11.72 C$ C$ cost to Purchase US$500 Commission US$1.00 = C$ ?

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 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$1.00 Calculate the cost in Canadian$ for the equivalent of 1 gallon of gas. Convert US$1.39 to C$. How much cheaper is the gas in Seattle?

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 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$ litres C$0.659 per litre = C$2.494 C$2.172 US$1.39 C$XC$X US$1.00 = C$ Cross - multiply C$X = C$ US$1.00 * US$1.39 C$ = C$0.322 cheaper = C$2.172

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© 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$C$ C$1.00 = DM C$1.00 = DM DM1 = 1 = C$ DM 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 LO 5.

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Ratios Proportions Ratios Proportions 3 3 McGraw-Hill Ryerson© This completes Chapter 3 Mcgraw-Hill Ryerson©

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