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Proportion Graphing Activity
Monday, December 16, 2012
5-4 Dimensional Analysis
Problem of the Day
The sum of four consecutive integers is 182. What
are the four numbers?
44, 45, 46, and 47
Course 2
Proportional???
6-4 Solving Equations Containing Percents
Sloths may seem lazy, but their extremely slow movement
helps to make them almost invisible to predators. Sloths sleep
an average of 16.5 hours a day. To find out what percent of a
24-hour day 16.5 hours is, you can use a proportion or an
equation.
Course 2
6-4 Solving Equations Containing Percents
Proportion Method
Part
Whole
n
= 16.5
24
100
Equation Method
Part
Whole
n · 24 = 100 · 16.5
24n = 1,650
n = 68.75
Sloths spend about 69% of the day sleeping!
Course 2
What percent of 24 is 16.5?
n
· 24 = 16.5
n = 0.6875
n = 68.75%
6-4 Solving Equations Containing Percents
Additional Example 1A: Using Proportions to Solve
Problems with Percents
Solve.
A. 25 is what percent of 40?
n = 25
Write a proportion.
100
40
n · 40 = 100 · 25
40n = 2,500
40n = 2,500
40
40
n = 62.5
25 is 62.5% of 40.
Course 2
Set the cross products equal.
Multiply.
Divide each side by 40 to isolate
the variable.
6-4 Solving Equations Containing Percents
Additional Example 1B: Using Proportions to Solve
Problems with Percents
Solve.
B. 15 is 25% of what number?
25 =
100
15
n
n · 25 = 100 · 15
25n = 1,500
25n = 1,500
25
25
n = 60
15 is 25% of 60.
Course 2
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 25 to isolate
the variable.
6-4 Solving Equations Containing Percents
Try This: Example 1A
Solve.
A. 10 is what percent of 50?
n = 10
Write a proportion.
100
50
n · 50 = 100 · 10
50n = 1,000
50n = 1,000
50
50
n = 20
10 is 20% of 50.
Course 2
Set the cross products equal.
Multiply.
Divide each side by 40 to isolate
the variable.
6-4 Solving Equations Containing Percents
Try This: Example 1B
Solve.
B. 8 is 40% of what number?
40 =
100
8
n
n · 40 = 100 · 8
40n = 800
40n = 800
40
40
n = 20
8 is 40% of 20.
Course 2
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 25 to isolate
the variable.
6-4 Solving Equations Containing Percents
Additional Example 2A: Using Equations to Solve
Problems with Percents
Solve.
A. 35 is 28% of what number?
35 = 28% · n
Write an equation.
35 = 0.28 · n
Write 28% as a decimal.
35 =
0.28
0.28 · n
0.28
125 = n
35 is 28% of 125.
Course 2
Divide each side by 0.28 to isolate the
variable.
6-4 Solving Equations Containing Percents
Additional Example 2B: Using Equations to Solve
Problems with Percents
Solve.
B. 18 is what percent of 9?
18 = n · 9
18 = n · 9
9
9
2=n
200% = n
18 is 200% of 9.
Course 2
Write an equation.
Divide each side by 9 to isolate the
variable.
Write the decimal as a percent.
6-4 Solving Equations Containing Percents
Try This: Example 2A
Solve.
A. 36 is 24% of what number?
36 = 24% · n
Write an equation.
36 = 0.24 · n
Write 24% as a decimal.
36 =
0.24
0.24 · n
0.24
150 = n
36 is 24% of 150.
Course 2
Divide each side by 0.24 to isolate the
variable.
6-4 Solving Equations Containing Percents
Try This: Example 2B
Solve.
B. 36 is what percent of 6?
36 = n · 6
36 = n · 6
6
6
6=n
600% = n
36 is 600% of 6.
Course 2
Write an equation.
Divide each side by 6 to isolate the
variable.
Write the decimal as a percent.
6-4 Solving Equations Containing Percents
Additional Example 3: Social Studies Application
Workers in Canada earn 10 vacation days, and workers in
Finland earn 30 vacation days. What percent of the vacation
days that workers in Canada earn do workers in Finland earn?
Restate the question: What percent of 10 is 30?
n · 10 = 30
Write an equation.
n · 10 = 30
Divide each side by 10 to isolate the
10
10
variable.
n = 3.0
n = 300
Write the decimal as a percent.
Workers in Finland earn 300% of the number of vacation
days that workers in Canada earn.
Course 2
6-4 Solving Equations Containing Percents
Try This: Example 3
Workers in Canada earn 10 vacation days, and workers in
Britain earn 20 vacation days. What percent of the vacation
days that workers in Canada earn do workers in Britain earn?
Restate the question: What percent of 10 is 20?
n · 10 = 20
Write an equation.
n · 10 = 20
Divide each side by 10 to isolate the
10
10
variable.
n = 2.0
Write the decimal as a percent.
n = 200
Workers in Britain earn 200% of the number of vacation days
that workers in Canada earn.
Course 2
Containing
6-4 Solving
Insert Equations
Lesson Title
Here Percents
Lesson Quiz
1. 21 is 42% of what number?
2. 73 is what percent of 292?
3. 112% of what number is 84?
4. 13.4 is what percent of 1340?
50
25%
75
1%
5. An ad shows a DVD player on sale for 75% of its original
price. If its original price was $242, what is the sale price?
$181.50
Course 2
Homework