Transcript Holt Algebra 1 2-9

2-9
Application of Percents
Warm Up
1. Write 0.03 as a percent. 3%
2. Write
as a decimal. 0.045
Find each value. Round to the nearest tenth
if necessary.
3. Find 10% of 53. 5.3 4. Find
of 50. 1.25
Solve for x.
5. 40 = (x)
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(20) 4
6. 114 = (36)
(x) 38
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Application of Percents
Objectives
Use common applications of percents.
Estimate with percents.
Holt Algebra 1
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Application of Percents
Vocabulary
commission
interest
sales tax
principal
tip
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Application of Percents
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.
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Application of Percents
Caution!
You must convert a percent to a
decimal or a fraction before doing any
calculations with it.
Holt Algebra 1
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Application of Percents
Example 1: Business Application
Mr. Cortez earns a base salary of $26,000 plus
a sales commission of 5%. His total sales for
one year were $300,000. Find his total pay for
the year.
Write
the formula for total pay.
total pay = base salary
+ commission
the formula
= base + %Write
of total
sales for commission.
values given in the problem.
= 26,000 Substitute
+ 5% of 300,000
the percent as a decimal.
= 26,000 + Write
(0.05)(300,000)
= 26,000 + 15,000
Multiply.
= 41,000 Add.
Mr. Cortez’s total pay was $41,000.
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Application of Percents
Check It Out! Example 1
A telemarketer earns $350 per week plus
12% commission on sales. Find her total pay
for a week in which her sales were $940.
Write
the formula for total pay.
total pay = base salary
+ commission
the formula
= base + %Write
of total
sales for commission.
Substitute
values given in the problem.
= 350 + 12%
of 940
Write the percent as a decimal.
= 350 + (0.12)(940)
= 350 + 112.80
Multiply.
= 462.80 Add.
The telemarketer’s total pay was $462.80.
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Application of Percents
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.
Simple Interest Paid Annually
Time in years
Simple interest
Principal
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Interest rate per
year as a decimal
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Application of Percents
Example 2A: Financial Application
Find the simple interest paid for 3 years on
a $2500 loan at 11.5% per year.
I = Prt
I = (2500)(0.115)(3)
I = 862.50
Write the formula for simple
interest.
Substitute known values.
Write the interest rate as a
decimal.
Multiply.
The amount of interest is $862.50.
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Application of Percents
Example 2B: Financial Application
After 6 months, the simple interest earned
on an investment of $5000 was $45. Find
the interest rate.
Write the formula for simple
I = Prt
interest.
Substitute the given values.
45 = 2500r
0.018 = r
The interest rate is 1.8%.
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Multiply 5000
.. Since r is
multiplied by 2500, divide
both sides by 2500 to undo
the multiplication.
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Application of Percents
Helpful Hint
When you are using the formula I= Prt to find
simple interest paid annually, t represents
time in years. One month is
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year.
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Application of Percents
Check It Out! Example 2a
Find the simple interest earned after 2
years on an investment of $3000 at 4.5%
interest earned annually.
I = Prt
Write the formula for simple
interest.
I = (3000)(0.045)(2)
Substitute the given values.
I = 270
Multiply.
The interest earned is $270.
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Application of Percents
Check It Out! Example 2b
The simple interest paid on a loan after 6
months was $306. The annual interest rate
was 8%. Find the principal.
I = Prt
306 = (P)(0.08)
306 =.04P
Write the formula for simple
interest.
Substitute the given values.
Multiply 0.08
. Since P is
multiplied by 0.04 , divide
both sides by 0.04.
7650 = P
The remaining principal is $7650.
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Application of Percents
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 item’s cost.
Holt Algebra 1
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Application of Percents
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
of the number.
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of 10%
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Application of Percents
Example 3A: Estimating with Percents
Lunch at a restaurant is $27.88. Estimate a
15% tip.
Step 1 First round $27.88 to $30.
Step 2 Think: 15% = 10% + 5% Move the decimal
point one place left.
10% of $30 = $3.00
Step 3 Think 5% = 10% ÷ 2
= $3.00 ÷ 2 = $1.50
Step 4 15 = 10% + 5%
= $3.00 + $1.50 = $4.50
The tip should be about $4.50.
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Application of Percents
Example 3B: Estimating with Percents
The sales tax rate is 7.25%. Estimate the sales
tax on a book that costs $19.97.
Step 1 First round 7.25% to 7% and
$19.97 to $20.
Step 2 Think: 7% = 7(1%)
1% of $20 =$0.20
Step 3 7% = 7(1%)
= 7($0.20) = $1.40
The sales tax is about $1.40.
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Move the decimal
point two places left.
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Application of Percents
Helpful Hint
A 6.25% sales tax rate means that for
every $100 you spend, you would pay
$6.25 in sales tax.
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Application of Percents
Check It Out! Example 3a
Estimate a 15% tip on a check for $21.98.
Step 1 Think: 15% = 10% + 5%
10% of $22 = $2.20
Move the decimal
point one place left.
Step 2 Think 5% = 10% ÷ 2
$2.20 ÷ 2 = $1.10
Step 3 15% = 10% +5%
= $2.20 + $1.10 = $3.30
The tip should be about $3.30.
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Application of Percents
Check It Out! Example 3b
Estimate the tax on shoes that cost $68.50
when the sales tax rate is 8.25%.
Step 1 First round 8.25% to 8% and
$68.50 to $70.
Step 2 Think: 8% = 8(1%)
1% of $70 =$0.70
Step 3 8% = 8(1%)
= 8($0.70) = $5.60
The sales tax is about $5.60.
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Move the decimal
point two places left.
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Application of Percents
Lesson Quiz: Part 1
1. A computer salesperson earns a base salary of
$32,000 per year plus a commission of 6% on
total sales. Total sales for one year were
$350,000. Find the salesperson’s total pay for
the year. $53,000
2. Find the simple interest paid for 9 months on a
a $500 loan at 8% per year. $30
3. After 2 years the simple interest earned on an
investment of 4000 was $216. Find the interest
rate. 2.7%
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Application of Percents
Lesson Quiz: Part 2
4. A family’s dinner check was $38.82.
Estimate a 15% tip. About $6.00
5.The sales tax rate is 7.1%. Estimate
the sales tax on a television set that
costs $399. About $28
Holt Algebra 1