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
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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