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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.