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?