Transcript 3.8 Rates Ratios and Percents

Chapter 3 – Solving
Linear Equations
3.8 – Rates, Ratios, and Percents
3.8 – Rates, Ratios, and
Percents
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Today we will learn how to:
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Use rates and ratios to model and solve reallife problems
Use percents to model and solve real-life
problems
3.8 – Rates, Ratios, and Percents
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If you have two quantities with different
units, the RATE OF A per B is a/b.
Rates are commonly expressed as unit
rates.
A UNIT RATE is a rate per one unit.
3.8 – Interpreting Large Numbers
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Example 1
 Estimated spending in U.S. in 1996
 Find the cost per person, assuming the U.S.
population in 1996 was about 266 million.
Clothing &
$183 billion
Shoes
Restaurants
$190 billion
Food at home $300 billion
Solution
We need to find the average rate of spending per person so that
people can compare themselves to the average. You can do this by
dividing by the total population
Example 1 (cont)
Clothing & Shoes
$183 billion
 Restaurants
 $190 billion
 Food at Home
 $300 billion
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Clothing and shoes
$183/266=.68796
≈$688 per person
 Restaurants
$190/266=.71428
≈$714 per person
 Food at home
$300/266=1.127819
≈$1128 per person
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3.8 – Using Collected Data
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Example 2
 You have recorded your car
mileage and gasoline use
for 5 weeks. Estimate the
number of miles you can
drive on a full 12-gallon
tank of gasoline.
Number of
miles
159
Number of
gallons
5.0
237
195
215
183
6.9
6.0
6.5
5.7
Number Number
of miles of
gallons
Solution
Add up the total miles driven and total
number of gallons used to get an average of
miles per gallon. You drove a total of 989
miles and used 35.1 gallons of gas, so your
average rate was
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159
5.0
989 ÷35.1≈28.1 miles per gallon
237
6.9
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195
6.0
215
6.5
183
5.7
Let x represent the number of miles you
drive on 12 gallons.
Number of Miles →
x
Number of Gallons → 12
28.1 ←Average rate per gallon
X ÷12=28.2
The solution is x=337.2, so your estimate is
337 miles on an 12 gallon tank
3.8 – Applying Unit Analysis
Example 3
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You are visiting Mexico and you want to
exchange $180 for pesos. The rate of currency
exchange is 9.990 pesos per United States
dollar. You want to find out how many pesos
you will receive.
Unit Analysis-You can use unit analysis to
write an equation
Dollars ×pesos = pesos
180×9.990= P
1
1
1798.2= P- You will receive 1,798 Pesos
Example #5- Finding Percents
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What percent of 1517 year-olds said they
are dating?
Age
Group
Number
Number
Surveyed who are
dating
12-14 year 1074
old
216
15-17 year 992
old
482
18-19 year 307
old
205
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Solution:
To find the percent, divide
by the number who are
dating by the number
surveyed and then write the
result as a percent.
482 ÷992 ≈.485887097, so
about 49% of 15-17 yearolds said that they are
dating
3.8 – Rates, Ratios, and Percents
HOMEWORK
Page 183 & 184
#15-19, 23-27, 30-35 ALL