Algebra I Applications of Percents

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Algebra IApplications ofPercents
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Warm Up
1) Find 75 of 60.
1) 45
2) Find 115 of 80.
2) 92
3) What percent of 40 is 25?
3) 62.5
4) What percent of 225 is 135?
4) 60
5) 56 is what percent of 20?
5) 280
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Applications of Percent

• Sales representatives use percents to calculate
  their total pay.
• We can apply percent concepts to find the
  discount and sale price of an item. The discount
  rate is given as a percent.
• Percent concepts can be applied to compute
  percent increase and percent decrease of various
  items.
• We can apply percent concepts to solve problems
  of the form "One number is some percent of
  another number." by identifying the given
  information, setting up a proportion, and solving
  for the unknown value.

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A commission is money paid to a person or a
company for making a sale. Usually the commission
is a percent of the sale amount.
Interest is the amount of money charged for
borrowing money, or the amount of money earned
when saving or investing money. Principal is the
amount borrowed or invested. Simple interest is
interest paid only on the principal.
Formula for Simple Interest Paid Annually
Simple Interest, I P r t
Time in years
Interest rate per year as a decimal
Principal
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Business Application
A) Daniela earns a base salary of 40,000 plus a
2.5 commission on sales. Her total sales one
year were 800,000. Find her total pay for the
year.
SOLUTION
total pay base salary commission
Write the formula for total pay.
base salary of total sales
Write the formula for commission.
40,000 2.5 of 800,000
Substitute values given in the problem.
Next page ?
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40,000 2.5 of 800,000 100
40,000 (0.025)(800,000)
Write the percent as a decimal.
40,000 20,000
Add.
60,000
Daniela total pay was 60,000.
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Now you try!
Solve
1) A telemarketer earns 350 per week plus a 12
commission on sales. Find her total pay for a
week in which her sales are 950.
1) 350 114 464
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Finance Application
A) Find the simple interest paid annually for 3
years on a 1200 loan at 15 per year.
SOLUTION
I P r t
Write the formula for simple interest.
I (1200) (0.15) (2)
Substitute known values. Write the interest rate
as a decimal.
I 540
The amount of interest is 540.
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B) After 3 months the simple interest earned
annually on an investment of 7000 was 63. Find
the interest rate.
SOLUTION
When you are using the formula I P r t to find
simple interest paid annually, t represents time
in years. One month is 1 year. In the given
problem, t 3 . 12
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I P r t
Write the formula for simple interest.
63 (700) (r) (3) 12
Substitute known values.
Next page ?
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Multiply 7000 (3) . 12
63 1750r
63 1750r 1750 1750
Since r is multiplied by 1750, divide both sides
by 1750 to undo the multiplication.
0.036 r
The interest rate is 3.6.
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Now you try!
Solve
1) Find the simple interest earned after 2 years
on an investment of 3000 at 4.5 interest earned
annually.
1) 270
2) The simple interest paid on a loan after 6
months was 306. The annual interest rate was 8.
Find the principal.
2) 7650
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A tip is an amount of money added to a bill for
service. It is usually a percent of the bill
before sales tax is added. Sales tax is a
percent of an items cost.

• Sales tax and tips are sometimes estimated
  instead of calculated exactly. When estimating
  percents, use percents that you can calculate
  mentally.
• Find 10 of a number by moving the decimal point
  one place to the left.
• Find 1 of a number by moving the decimal point
  two places to the left.
• Find 5 of a number by finding 1 of 10 of the
  number.
• 2

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Estimating with Percents
A) The dinner check for Marias family is 67.95.
Estimate a 15 tip.
SOLUTION
Step 1 First round 67.95 to 70.
Step 2 Think 15 10 5
10 of 70 7.00
Move the decimal point one place left.
Step 3 Think 5 10 2
7.00 2
3.50
Step 4 15 10 5 7.00 3.50
10.50
The tip should be about 10.50.
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Estimating with Percents
B) The sales tax rate is 6.25. Estimate the
sales tax on a shirt that costs 29.50.
SOLUTION
Step 1 First round 6.25 to 6 and 29.50 to 30
Step 2 Think 6 6 (1) 1 of 30
0.30
Move the decimal point two places to the left.
Step 3 6 6 (1)
6 (0.30) 1.80
The sales tax is about 1.80.
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Now you try!
Solve
1) Estimate a 15 tip on a check for 21.98.
1) 3.3
2) Estimate the tax on shoes that cost 68.50
when the sales tax rate is 8.25.
2) 5.52
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Some more examples
A) Two candidates A and B contest an election. A
gets 46 of the valid votes and is defeated by
1600 votes. Find the total number of valid votes
cast in the election?
SOLUTION
A gets 46 of the valid votes.
B gets (100 46) 54 of the valid votes.
Therefore, difference if the votes by which A
is defeated is 54 - 46 8.
8 of the total valid votes cast 1600.
i.e. 8 of the total votes 1600. 100
Total number of valid votes cast 100 1600
20,000
8
Total number of valid votes cast is 20,000
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B) My income was increased by 10 and later
decreased by 10. What is the total change in the
percent in my income?
SOLUTION
Let my income be 100.
10 increase means that my income becomes 110.
Decreased income 110 - 10 110
100
110 - 11 99.
change in income Change in income 100
original income

100 - 99 100 1
100
The percent in my income is 1.
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Now you try!
Solve
1) What percent of votes are in favor of a
candidate if 25 persons vote for him and 45
persons vote against him?
1) 35.7
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Assessment
1) A sales representative earns a 2.5 commission
on sales. Find the commission earned when the
total sales are 80,700.
1) 2017.5
2) A man spends 45 of his income and saves 2640
in a month. What is his monthly income?
2) 4800
3) Karen earns a salary of 28,600 per year plus
a 4.25 commission on sales. Find her total
salary for a year when the sales are 310,000.
3) 42550
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4) Find the amount of simple interest earned
after 2 years on 480 invested at a 7 annual
interest rate.
4) 67.2
5) Find the number of years it would take for
1200 to earn simple interest of 324 at an
annual interest rate of 6 per year.
5) 4.5 years
6) Find the total amount owed after 6 months on a
loan of 900 at an annual interest rate of 8.5.
6) 229.5
7) Estimate the tip on a 42.65 check using a tip
rate of 15.
7) 6.45
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8) Estimate the tax on a 198 stereo when the
sales tax is 5.25.
8) 10
9) The weight of the box by mistake was written
as 21 kg, while it was 25 kg. What is the error .
9) 16
10) A boy remains awake for 16 hrs a day. For
what percentage of the time does he sleep?
10) 33.33
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Lets review
A commission is money paid to a person or a
company for making a sale. Usually the commission
is a percent of the sale amount.
Interest is the amount of money charged for
borrowing money, or the amount of money earned
when saving or investing money. Principal is the
amount borrowed or invested. Simple interest is
interest paid only on the principal.
Formula for Simple Interest Paid Annually
Simple Interest, I P r t
Time in years
Interest rate per year as a decimal
Principal
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review
Business Application
A) Daniela earns a base salary of 40,000 plus a
2.5 commission on sales. Her total sales one
year were 800,000. Find her total pay for the
year.
SOLUTION
total pay base salary commission
Write the formula for total pay.
base salary of total sales
Write the formula for commission.
40,000 2.5 of 800,000
Substitute values given in the problem.
Next page ?
24
review
40,000 2.5 of 800,000 100
40,000 (0.025)(800,000)
Write the percent as a decimal.
40,000 20,000
Add.
60,000
Daniela total pay was 60,000.
25
review
Finance Application
A) Find the simple interest paid annually for 3
years on a 1200 loan at 15 per year.
SOLUTION
I P r t
Write the formula for simple interest.
I (1200) (0.15) (2)
Substitute known values. Write the interest rate
as a decimal.
I 540
The amount of interest is 540.
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Estimating with Percents
A) The dinner check for Marias family is 67.95.
Estimate a 15 tip.
SOLUTION
Step 1 First round 67.95 to 70.
Step 2 Think 15 10 5
10 of 70 7.00
Move the decimal point one place left.
Step 3 Think 5 10 2
7.00 2
3.50
Step 4 15 10 5 7.00 3.50
10.50
The tip should be about 10.50.
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review
Estimating with Percents
B) The sales tax rate is 6.25. Estimate the
sales tax on a shirt that costs 29.50.
SOLUTION
Step 1 First round 6.25 to 6 and 29.50 to 30
Step 2 Think 6 6 (1) 1 of 30
0.30
Move the decimal point two places to the left.
Step 3 6 6 (1)
6 (0.30) 1.80
The sales tax is about 1.80.
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Some more examples
review
A) Two candidates A and B contest an election. A
gets 46 of the valid votes and is defeated by
1600 votes. Find the total number of valid votes
cast in the election?
SOLUTION
A gets 46 of the valid votes.
B gets (100 46) 54 of the valid votes.
Therefore, difference if the votes by which A
is defeated is 54 - 46 8.
8 of the total valid votes cast 1600.
i.e. 8 of the total votes 1600. 100
Total number of valid votes cast 100 1600
20,000
8
Total number of valid votes cast is 20,000
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review
B) My income was increased by 10 and later
decreased by 10. What is the total change in the
percent in my income?
SOLUTION
Let my income be 100.
10 increase means that my income becomes 110.
Decreased income 110 - 10 110
100
110 - 11 99.
change in income Change in income 100
original income

100 - 99 100 1
100
The percent in my income is 1.
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