MATHEMATICAL EXCURSIONS Math and the Tourist

Transcription

1 MATHEMATICAL EXCURSIONS Math and the Tourist When you travel to a foreign country, besides different languages and customs, you may encounter a different currency, system of weights and measures, and temperature scale. You may have to convert dollars to euros or yen. You may wonder how fast you are traveling when the speedometer reads km/hr. You may think you have lost weight when a bathroom scale reads 72 kg. You may ponder how to set the air conditioner s thermostat when you have a choice of temperatures from 10 to 30. The goal of this section is to show you the mathematics necessary to handle the different currency, system of weights and measures, and temperature scale that a tourist might encounter. Currency The table below gives the value of an U.S. dollar in the currencies of various foreign countries. One U.S. dollar equals the following: Australian Dollar New Zealand Dollar Brazilian Real 2.22 Norwegian Kroner British Pound Singapore Dollar Canadian Dollar South African Rand Chinese Yuan South Korean Won Danish Krone Sri Lanka Rupee Euro Swedish Krona 7.60 Hong Kong Dollar Swiss Franc Indian Rupee Taiwan Dollar 32.3 Japanese Yen Thai Baht Malaysian Ringgit 3.76 Venezuelan Bolivar Mexican Peso (rates as of /1/0) Current values can be found on the internet at For the purpose of explaining a method to work with different currencies, we use the values given in the above table. Example 1 How many euros do you get for $7 U.S.? Solution: A straight forward way to handle currency conversions is to use a proportion involving the ratio of U. S. dollars and the foreign currency. From the chart, we get the ratio of the U.S. dollar to a euro of 1: page

2 Let x the number of euros for $7 U.S. U.S. dollar U.S. dollar euro euro x 1 x 7( ) x Thus, $7 will get you (euros). Example 2 If your have 200 (Japanese yen), how much do you have in U.S. dollars? Solution: Using the ratio between the U.S. dollar and yen of 1 : , and letting x the amount in U.S. dollars, we have the following. Example 3 U.S. dollar yen x U.S. dollar yen x x (divide both sides by ) Thus, you have an equivalent of $22.4 in U.S. dollars. While vacationing in Venezuela, you put the cost of 71,60 bolivars for a dinner on your VISA card. How much (in U. S. dollars) was charged to your VISA account? Solution: Using the ratio of the U.S. dollar and bolivar of 1:2144.6, and letting x the amount in U.S. dollars, we have the following. U.S. dollar U.S. dollar bolivar bolivar 1 x , x 71, 60 x (cross multiply the proportion) (divide both sides by ) Thus, $33.37 was charged to your VISA account. Weights and Measures Many foreign countries use the metric system for weights and measures rather that the U.S. customary system. In the U.S. you may be familiar with some of the metric measures. For example, soft drinks come in liter bottles, you may take a 200 mg (milligram) tablet of vitamin page 100

3 page 101 C, or you may run a 10K (10 kilometer) race. In a foreign country you will encounter these and other metric measurements. We will examine some of the more common ones in this section. The chart below gives some of the most used conversions between the U.S. customary system and the Metric system of weights and measures. Example 4 U.S. METRIC Length 1 in. (inch) 2.4 cm (centimeter) 3.4 in. (inch) 1 m (meter) mi (mile) 1 km (kilometer) Weight 1 oz (ounce) 28.3 g (gram) 2.2 lb (pound) 1 kg (kilogram) Volume 1.06 qt (quart) 1 l (liter) When a bathroom scale in Canada indicates that your mass is 72 kg, what is that amount in pounds? Solution: Set up and solve a proportion comparing the ratio of kilogram to pound, 1 : 2.2. Example Let x the weight in pounds kg kg lb lb x x Thus, your weight is 18.4 lbs in the U.S. system. While driving on the German autobahn, you notice that you reached a speed of km/hr. How fast were you traveling in miles per hour? Solution: We set up and solve a proportion comparing the ratios of kilometers to miles, 1 : and let x the number of miles. Temperature km km mi mi x x. 0 You were traveling about mi/hr. Besides differences in the currency and units of weights and measures used in a foreign country, a tourist may also encounter an unfamiliar system for measuring temperature. In the

4 United States, we commonly use the Fahrenheit Scale ( F) where water freezes and 32 F and boils at 212 F. Many countries use the Celsius Scale ( C) where water freezes at 0 C and boils at 100 C. If you do not have experience with the Celsius Scale, you might find it difficult to relate to a temperature reading. The rhyme that follows might give you some feel for the outside temperature in the Celsius Scale: 30 is hot, 20 is nice, 10 is cool, 0 is ice. If, however, you want to know the exact relation between a Celsius reading and a Fahrenheit reading, there is a formula that converts temperatures from one scale to the other. F Fahrenheit reading F C+ 32 where C Celsius reading Let s see how this formula is used. Example 6 If the outside temperature is 30 C what is the equivalent Fahrenheit temperature? Solution: If we put C 30 in the above formula, we can find the Fahrenheit temperature. Example 7 The air conditioning unit in your hotel room in Canada has a Celsius scale on its thermostat, what should you set it at if you feel comfortable when the temperature is 70 F? Solution: If we put F 70 in the formula, we can solve for the Celsius temperature. F C C C ( ) C C You should set the air conditioning unit at about 21 C. There are other ways to solve currency and weight and measure conversions but using proportions is a straightforward way to do all these types of problems and using the Fahrenheit-Celsius formula is a good way to convert temperature readings. So when you become a tourist, take along your calculator and your ability to solve proportions and equations and you ll be math prepared. page 102

5 Exercises 1. Explain how proportions are used to convert between different currencies. 2. Explain how proportions are used to convert between U.S. customary and metric weights and measures. 3. If you exchange $400 U.S. into each of the following currencies, how much would you receive in that currency? a) Chinese Yuan b) South Korean Won c) British Pound d) New Zealand Dollar 4. If you have 400 of the following currencies, how many U.S. dollars do you have? a) Australian Dollar b) Danish Krone c) Taiwan Dollar d) Sri Lanka Rupee. You put your three night Mexico City hotel bill of 227 pesos on your MasterCard. How many U.S. dollars is charged to your MasterCard account? 6. The tag on a pair of shoes in a store in Florence, Italy, says you are paying $8 U.S. but they charge you 0 euros. Using the exchange rates given, how much were you overcharged? 7. You purchase a picture frame in Copenhagen, Denmark, that holds a 20 by 2 cm photograph. Approximately what size photograph is that in U.S. measurements. 8. A road sign in Canada says Alberta, 270 km. How far is that in miles?. You fill your rental car in Berlin, Germany, with 8.6 liters at 1.37 euros per liter. a) How many gallons of gasoline did you put into the car? b) What is the cost of the gasoline in euros and in U.S. dollars? c) How much did the gasoline cost per gallon in U.S. dollars? 10. You purchase 4. meters of fabric in Stockholm, Sweden for 16 Krona. a) How many yards of fabric did you buy? b) What is the cost of the fabric in U.S. dollars? c) What is the cost per yard in U.S. dollars? 11. To ship an item from New Delhi, India, to the United States, costs rupee per kilogram. You plan to ship an item that weighs 24 pounds. a) How many kilograms are you shipping? b) What is the range of the shipping cost in rupees? c) What is the range of the shipping cost in U.S. dollars? 12. Find the outside temperature on the Fahrenheit scale, when the thermometer reads 2 C. 13. Find the correct Celsius setting if you want to cook a roast at 30 F. 14. Are you running a fever if the Celsius scale on the thermometer reads 40.1 C? page 103