9/5/11 +
+
Ratios

Way to compare two quantities, usually parts to parts.

Ex: ratio of women to men in a room is 4 to 5.

If there are 125 men in the room, how many women are there?
Proportion

An expression that says that two ratios are equal is called a
proportion.
if
1 9/5/11 Before the oil spill in Liberty park lake lived
ducks and geese. Their ratio was 16 ducks to 9
geese. How many of each kind of bird were there
is the total number of them was 300?
How would you find out how many
fish live in a lake?
2 9/5/11 Biologists need to know roughly how many fish
live in a certain lake, but they don't want to stress
or otherwise harm the fish by draining or
dragnetting the lake. Instead, they let down small
nets in a few different spots around the lake,
catching, tagging, and releasing 96 fish. A week
later, after the tagged fish have had a chance to
mix with the general population, the biologists
come back and let down their nets again. They
catch 72 fish, of which 4 are tagged. Assuming
that the catch is representative, how many fish
live in the lake?
+
2.3 Applications of Linear Equations
Solve business-related problems.
Solve mixture problems.
Solve classic rate problems
Use formulas to solve application problems.
3 9/5/11 Problem Solving Practice
A salesperson told you that a pot and a lid
cost $11 together and that the pot costs $10
more than the lid. How much is the pot and
how much is the lid?
The bill for the repair of your car was
$210. The cost for parts was $162. The
cost for labor was $32 per hour. How
many hours did the repair work take?
4 9/5/11 The velocity v of an object projected
vertically upward with an initial velocity of
64 feet/sec is given by v=64-32t, where t is
the time in seconds. When does the object
reach its maximum height?
You went out with some friends and your
portion of the bill ended up being $18. The
service wasn’t too great, but it wasn’t
terrible either, so you decide that 15%
should be good enough tip. How much did
the waiter get from you?
5 9/5/11 I bought a computer for $1650 and was told
that I received a 15% educator discount.
What was the original price of my
computer?
Just before I got a 10% raise three months
ago my salary had been $62000.
Unfortunately my company went through
some rough times (I work in real estate
business), and I had to take 10% salary cut.
What happened to my salary?
6 9/5/11 You ride your bike at an average speed of 16
miles per hour. How long will it take you to
ride 20 miles?
Two cars start at the same location and
travel in the same direction at average
speeds of 30 miles per hour and 45 miles
per hour. How much time must elapse
before they are 5 miles apart?
7 9/5/11 A department store sells a pair of jeans
for $60. The cost of the jeans is $35.
What is the markup rate?
The jeans go on sale for 40% off. What
is the discount? Does the store make
any money on the jean during the
sale?
The cooling system on a truck contains 5
gallons of coolant that is 40% antifreeze.
How much must be withdrawn and
replaced with 100% antifreeze to bring
the coolant in the system to 50%
antifreeze?
8 9/5/11 You can mow a lawn in 3 hours, and your
friend can mow the same law in 4hours.
How long will it take you to mow the
lawn working together?
Solve for b:
9 9/5/11 Find the annual interest rate on a
certificate of deposit that accumulated
$400 interest in 2 years on a principal
of $2500. (Assume simple interest.)
+
2.4: Linear Inequalities

Graph inequalities.

Identify and use the properties of inequalities.

Solve linear inequalities.

Solve compound inequalities.

Solve application problems involving inequalities.
10 9/5/11 + Graph the following inequalities
+
Write inequalities whose graphs are
given
-4
-4
-4
-3
-3
-3
-2
-2
-2
-1
-1
-1
0
0
0
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
11 9/5/11 + Solve the inequality and sketch the
solution on the real number line:
−6 ≤ 9 − 3x < 0
€
+
2.5: Absolute Value Equations and
Inequalities.

Solve absolute value equations.

Solve inequalities involving absolute value.
12 9/5/11 +
+
Compare the following…
Absolute value
 Geometric
Definition
  |p|
is the distance of p from the origin on a
number line.
 Algebraic
Definition
  We
can also give a strict mathematical/
formula definition for absolute value. It is,
13 9/5/11 + Write an inequality that represents the
following statements
1.
The set of all real numbers x whose distance from 0 is less than 3.
2.
The set of all real numbers whose distance from 5 is more than 6.
3.
The set of all real numbers whose distance from -3 is no more than 4.
+
Solve each equation.
14 9/5/11 +
+
Solve each equation.
Solve each inequality.
15 9/5/11 +
Solve each inequality.
16