# MATHEMATICAL EXCURSIONS Math and the Tourist

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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

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