6-5 solving percent problems course 2 warm up warm up problem of the day problem of the day lesson...
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6-5 Solving Percent Problems
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpSolve.
1. 4x = 90
2. 8x = 96
3. 12x = 180
4. 26x = 182
22.5
12
15
Course 2
6-5 Solving Percents Problems
7
Problem of the Day
Rearrange the digits in . What
fraction of the possible arrangements are true proportions?
26
= 13
13
Course 2
6-5 Solving Percents Problems
Learn to solve problems involving percents.
Course 2
6-5 Solving Percents Problems
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
6-5 Solving Percents Problems
Proportion Method Equation Method
n100
= 16.524
PartWhole
PartWhole
What percent of 24 is 16.5?
n · 24 = 100 · 16.5
24n = 1,650
n = 68.75
n · 24 = 16.5
n = 0.6875
n = 68.75%
Sloths spend about 69% of the day sleeping!
Course 2
6-5 Solving Percents Problems
Solve.
Additional Example 1A: Using Proportions to Solve Problems with Percents
What percent of 40 is 25?n
100= 25
40
n · 40 = 100 · 25
40n = 2,500
40n40
= 2,500 40
n = 62.5
25 is 62.5% of 40.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 40 to isolatethe variable.
Course 2
6-5 Solving Percents Problems
Solve.
Additional Example 1B: Using Proportions to Solve Problems with Percents
15 is 25% of what number?
25100
= 15n
n · 25 = 100 · 15
25n = 1,500
25n25
= 1,500 25
n = 60
15 is 25% of 60.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 25 to isolatethe variable.
Course 2
6-5 Solving Percents Problems
Solve.
Check It Out: Example 1A
What percent of 50 is 10?n
100= 10
50
n · 50 = 100 · 10
50n = 1,000
50n50
= 1,000 50
n = 20
10 is 20% of 50.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 50 to isolatethe variable.
Course 2
6-5 Solving Percents Problems
Solve.
Check It Out: Example 1B
8 is 40% of what number?
40100
= 8n
n · 40 = 100 · 8
40n = 800
40n40
= 800 40
n = 20
8 is 40% of 20.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 40 to isolatethe variable.
Course 2
6-5 Solving Percents Problems
Solve.
Additional Example 2A: Using Equations to Solve Problems with Percents
35 is 28% of what number?
35 = 28% · n
35 = 0.28 · n
350.28
= 0.28 · n0.28
125 = n
35 is 28% of 125.
Write an equation.
Write 28% as a decimal.
Divide each side by 0.28 to isolate the variable.
Course 2
6-5 Solving Percents Problems
Solve.
Additional Example 2B: Using Equations to Solve Problems with Percents
What percent of 9 is 18?
18 = n · 9
189
= n · 99
2 = n
200% = n
18 is 200% of 9.
Write an equation.Divide each side by 9 to isolate the variable.Write the decimal as a percent.
Course 2
6-5 Solving Percents Problems
Solve.
Check It Out: Example 2A
36 is 24% of what number?
36 = 24% · n
36 = 0.24 · n
150 = n
36 is 24% of 150.
Write an equation.
Write 24% as a decimal.
Divide each side by 0.24 to isolate the variable.
360.24
= 0.24 · n0.24
Course 2
6-5 Solving Percents Problems
Solve.
Check It Out: Example 2B
What percent of 6 is 36?
36 = n · 6
366
= n · 66
6 = n
600% = n
36 is 600% of 6.
Write an equation.Divide each side by 6 to isolate the variable.Write the decimal as a percent.
Course 2
6-5 Solving Percents Problems
A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18?
Additional Example 3: Finding Sales Tax
n100
= 18225
n · 225 = 100 · 18
8% of $225 is $18. The sales tax is 8%.
Write a proportion.
Set the cross products equal.
Multiply.
Restate the question: What percent of $225 is $18?
225n = 1800
Course 2
6-5 Solving Percents Problems
225n225
= 1800225
Divide each side by 225.
n = 8
A new flat screen TV costs $800 before tax at an appliance warehouse. What is the sales tax rate if the tax is $56?
Check It Out: Example 3
n100
= 56800
n · 800 = 100 · 56
7% of $800 is $56. The sales tax is 7%.
Write a proportion.
Set the cross products equal.
Multiply.
Restate the question: What percent of $800 is $56?
800n = 5600
Course 2
6-5 Solving Percents Problems
800n800
= 5600 800
Divide each side by 800.
n = 7
Lesson QuizSolve.
1. 21 is 42% of what number?
2. What percent of 292 is 73?
3. 112% of what number is 84?
4. What percent of 1,340 is 13.4?
5. An ad features a bicycle on sale for $139. If the total cost of the bike is $147.34, what is the sales tax rate?
25%
50
Insert Lesson Title Here
75
1%
6%
Course 2
6-5 Solving Percents Problems