Algebra II/Trig Honors Unit 5 Day 6: Rational Word Problems Objective: To solve rational word problems Example 1: Given a Function From 1995 through 2003, the annual sales S (in billions of dollars) of entertainment software can be 848t 2 3220 modeled by S t , 0 t 8 where t is the number of years since 1995. For which year 115t 2 1000 were the total sales of entertainment software about $5.3 billion? Example 2: Percent Problems An alloy is formed by mixing two or more metals. Sterling silver is an alloy composed of 92.5% silver and 7.5% copper by weight. Jewelry silver is composed of 80% silver and 20% copper by weight. How much pure silver should be mixed with 15 ounces of jewelry silver to make sterling silver? Percent of copper in mixture = Weight of copper in mixture Total weight of mixture Example 3: Distance, Rate, and Time Problems You drove halfway from Point A to Point B at 40 mi/h and the rest of the way at 60 mi/h. What was the average speed of the whole trip if the distance between the two locations is 100 mi? Example 3: Job Problems Pipe A can fill a tank in 5 hours. Pipe B can fill it in 2 less hours than pipe C, a drainpipe that can empty the tank. With all three pipes open, it takes 3 hours to fill the tank. How long would it take pipe C to empty a filled tank? Example 4: Calculator Problems Let x be the number of years since 1998, let g (x ) be the average monthly bill (in dollars) for mobile phone users in the United States, and let h(x) be the average number of minutes used by U.S. mobile phone users. The functions are given below. g ( x) 0.27 x 3 1.40 x 2 1.05 x 39.4 h( x) 8.25 x 3 53.1x 2 7.82 x 138 Write a rational function f (x ) that gives the average price per minute x years after 1998. Find the average price per minute in 1998. In what year did the average price per minute fall to 11 cents? Page 350 #33-36, and additional problems