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Algebra IA – Chapter 2 Problems for Today

Solve and check your answer.

2-1: Solve one-step equations in one variable by using addition or subtraction.

1

1.8 3n 1.8 3

1.8 1.8 3 1.8

1.2

n

n

n

1.8 1.2 3

3 3

Check.

Solve and check your answer.

2-2: Solve one-step equations in one variable by using multiplication or division.

2

27

w

27

( 7)( 2) ( 7)7

14

w

w

w

142

72 2

Check.

Solve and check your answer.

2-3: Solve equations in one variable that contain more than one operation.

3

15 23

a

15 23

15 2 2 23

(3)17 (3)3

51

a

a

a

a

5115 2

315 17 2

15 15

Check.

Solve.

2-4: Solve equations in one variable that contain variable terms on both sides.

4

2 1 11x x

2 1 11

2 1 11

1 11

1 1 11 1

12

x x

x x x x

x

x

x

The formula for the volume of a rectangular prism with length l, width w, and height h is:

Solve the formula for w.

2-5: Solve a formula for a given variable.

5

V lwh

V lwh

V lwh

lh lhV

wlh

Solve for s.

2-5: Solve an equation in two or more variables for one of the variables.

6

3 6st t

3 3 6 3

6 3

6 3

st t t t

st t

t tt

st

Find the unit rate.

2-6: Write and use ratios, rates, and unit rates.

7

2000

4050

A computer’s fan rotates 2000 times in 40 seconds.

rotations

seconds

rotations/second

Solve the proportion.

2-6: Write and solve proportions.

8

10 52

13h

10 52

1310(13) 52

130 52

130 52

52 522.5

hh

h

h

h

Find the value of x in the diagram.

2-7: Use proportions to solve problems involving geometric figures.

9

8

4 24 8(2)

x

x

4 16

4 16

4 44

x

x

x

Roger is 5 feet tall and casts a shadow 3.5 feet long. At the same time, the flagpole outside his school casts and shadow 14 feet long. Write and solve a proportion to find the height of the flagpole.

2-7: Use proportions and similar figures to measure objects indirectly.

10

5 3.5

143.5 5(14)

3.5 70

3.5 70

3.5 3.520

xx

x

x

x

The flagpole is 20 feet tall.

Find the value. Round to the nearest tenth if necessary.

2-8: Solve problems involving percents.

11

75% 0.75

0.75(40)

30

Find 75% of 40.

A sales representative earns a 2.5% commission on sales. Find the commission earned when the total sales are $80,700.

2-9: Use common applications of percents.

12

2.5% 0.025

0.025(80700)

2017.5

The commission earned on $80,700 is $2,017.50

13

Estimate a 15% tip on a $42.65 restaurant bill.

2-9: Estimate with percents.

10% of $42.65 is $4.2655% is half of $4.265 which is about $2.1315% is 10% + 5%$4.27 + $2.13 = $6.40A 15% tip on $42.65 is about $6.40.

Find the percent change. State whether it is a percent increase or decrease.

2-10: Find percent increase and decrease.

14

25 to 45

200.8

2580%

The change is an 80% increase.

Amount of change------------------------ Original amount

What is the final price on a $185 leather jacket that is on sale for 40% off?

2-10: Find percent increase and decrease.

15

100% 40% 60%

60% 0.6

0.6(185)

111

The final price of the jacket on sale for 40% off is $111.