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3.8 Rates, Ratios and Percents -We will use rates and ratios to model and solve real life world problems. -We will use percents to model and solve real life problems. Using Rates and Ratios • Rate of a per b is a/b. • Unit rate – Think of miles per gallon or $ per hour. Interpreting Large Numbers • Use unit rates to bring the numbers to something you can get a handle on. • Total US spending. Remember 300 million people live in the US. Clothing and shoes Restaurants Food at home Movie tickets $183 billion $190 billion $300 billion $10 billion Using collected data • How many miles can you drive on 18 gallons of gas based on the data you collected? # of miles 290 242 196 237 184 # of gallons 12.1 9.8 8.2 9.5 7.8 Unit Analysis • You are driving at 60 miles per hour. How many feet per minute are you driving? Converting money • Currently you can buy €.77 for $1. How many € can you get with $4000? • How many $ can you get with €4000? We will learn to solve proportions Proportions Solving Proportions Applications of Proportions 1. Read the problem and represent the unknown quantity by x. 2. Set up a proportion by listing the given ratio on one side and the ratio with the unknown quantity on the other side. 1. Make sure that similar values are in numerators and similar values are in the denominators. 3. Drop units and apply the cross products principle. 4. Solve for x and answer the question. Example of aligning a proportion correctly Example of aligning a proportion correctly • Unwritten rule of local politics is that for every lawn sign you place you can count on 12 votes. How many votes can someone who places 220 lawn signs expect to receive? Solving a Direct Variation Problem • A person works for $12/hr. The person works 15 hours, how much money does he earn?