CHAPTER 8
Consumer Mathematics
and Financial
Management
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8.1
Percent, Sales Tax, and Income Tax
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2.
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Objectives
Express a fraction as a percent.
Express a decimal as a percent.
Express a percent as a decimal.
Solve applied problems involving sales tax and
discounts.
Compute income tax.
Determine percent increase or decrease.
Investigate some of the ways percent can be abused.
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Basics of Percent
• Percents are the result of expressing numbers as a
part of 100.
• The word percent means per hundred.
Expressing a fraction as a percent:
1. Divide the numerator by the denominator.
2. Multiply the quotient by 100. This is done by
moving the decimal point in the quotient two places
to the right.
3. Add a percent sign.
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Example 1: Expressing a Fraction as a Percent
5
Express
as a percent.
8
Solution:
Step 1. Divide the numerator by the denominator.
5 ÷ 8 = 0.625
Step 2. Multiply the quotient by 100.
0.625  100 = 62.5
Step 3. Add a percent sign.
62.5%
5
Thus, = 62.5%.
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Expressing a Decimal as a Percent
To express a decimal as a percent:
1. Move the decimal point two places to the right.
2. Attach a percent sign.
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Example 2: Expressing a Decimal as a Percent
Express 0.47 as a percent.
Solution:
Thus, 0.47 = 47%.
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Expressing a Percent as a Decimal Number
To express a percent as a decimal number:
1. Move the decimal point two places to the left.
2. Remove the percent sign.
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Example 3: Expressing Percents as Decimals
Example: Express each percent as a decimal:
a. 19%
b. 180%
Solution: Use the two steps.
a.
Thus, 19% = 0.19.
b. 180% = 1.80 or 1.8
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Percent, Sales Tax, & Discounts
Many applications involving percent are based on the
following formula:
Note that “of” implies multiplication.
• We use this formula to determine sales tax collected
by states, counties, cities on sales items to customers.
Sales tax amount = tax rate  item’s cost
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Example 4: Percent and Sales Tax
Suppose that the local sales tax rate is 7.5% and you
purchase a bicycle for $894.
a. How much tax is paid?
b. What is the bicycle’s total cost?
Solution:
a. Sales tax amount = tax rate  item’s cost
7.5%  $894 = 0.075  $894 = $67.05
The tax paid is $67.05.
b. Total Cost = $894.00 + $67.05 = $961.05
The bicycle’s total cost is $961.05.
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Percent and Sales Price
• Businesses reduce prices, or discount, to attract
customers and to reduce inventory.
• The discount rate is a percent of the original price.
Discount amount = discount rate  original price.
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Example 5: Percent and Sales Price
A computer with an original price of $1460 is on sale at
15% off.
a. What is the discount amount?
b. What is the computer’s sale price?
Solution:
a. Discount amount = discount rate  original price
The discount amount is $219.
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Example 5: Percent and Sales Price continued
b. A computer’s sale price is the original price, $1460,
minus the discount amount, $219.
Sale price = $1460  $219 = $1241
The computer’s sale price is $1241.
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Percent and Income Tax
Calculating Income Tax:
1. Determine your adjusted gross income:
2. Determine your taxable income:
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Percent and Income Tax
3. Determine the income tax:
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Percent and Income Tax
• The table shows tax rates, standard deductions, and
exemptions for the four filing status categories.
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Example 6: Computing Income Tax
Example: Calculate the income tax owed by a single
woman with no dependents whose gross income,
adjustments, deductions, and credits are given. Use
the marginal tax rates from the table.
Single Woman with no dependents:
Gross income: $62,000
Adjustments: $4,000
Tax credit: $500
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Deductions:
• $7500: mortgage interest
• $2200: property taxes
• $2400: charitable contributions
• $1500: medical expenses not
covered the insurance
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Percent and Income Tax
Example Continued
Solution:
Step 1. Determine the adjusted gross income.
Adjusted gross income = Gross income – Adjustments
= $62,000  $4000
= $58,000
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Example 6 continued
Step 2. Determine taxable income.
We substitute $12,100 for deductions in the formula for taxable
income.
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Example 6 continued
Taxable income = Adjusted gross income – (Exemptions + Deductions)
– ($3500 + $12,100)
= $58,000 – $15,600
= $42,400
Step 3. Determine the income tax.
Income tax = Tax computation – Tax credits
= Tax Computation  $500
Since the single woman taxable income is $42,400 she
falls in the tax bracket of 25%.
= $58,000
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Example 6 continued
• This means that she owes:
10% on the first $8025 of her taxable income, 15% on
her taxable income between $8026 to $32,500,
inclusive, and 25% on her taxable income above
$32,550.
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Example 6 continued
= 0.10  $8025 + 0.15  ($32,550  $8025) + 0.25  ($42,400  $32,550)
= 0.10  $8025 + 0.15  ($24,525) + 0.25  $9850
= $802.50 + $3678.75 + $2462.50
= $6943.75
We substitute $6943.75 for the tax computation in the formula for
income tax.
Income tax = Tax computation – Tax credits
= $6943.75  $500
= $6443.75
Thus, the income tax owed is $6443.75.
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Percent and Change
If a quantity changes, its percent increase or its percent
decrease can be found as follows:
1. Find the fraction for the percent increase or decrease:
amount of increase
original amount
amount of decrease
or
.
original amount
2. Find the percent increase or decrease by expressing
the fraction in step 1 as a percent.
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Example 7: Finding Percent Increase and
Decrease
In 2000, world population was approximately 6 billion.
The data are from United Nations Family Planning
Program and are based on optimistic or pessimistic
expectations for successful control of human population
growth.
a. Find the percent increase in
world population from 2000 to
2150 using the high projection
data.
b. Find the percent decrease in
world population from 2000 to
2150 using the low projection
data.
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Example 7: Finding Percent Increase and
Decrease continued
Solution:
a. Use the data shown on the blue, high-projection,
graph.
The projected percent increase in world population is
400%.
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Example 7: Finding Percent Increase and
Decrease continued
b. Use the data shown on the green, low-projection,
graph.
amount of decrease
Percent decrease 
original amount
64 2 1
1

   33 %
6
6 3
3
The projected percent decrease in world population is
33⅓%.
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Example 9: Abuses of Percents
John Tesh, while he was still co-anchoring Entertainment
Tonight, reported that the PBS series The Civil War had an
audience of 13% versus the usual 4% PBS audience, “an increase
of more than 300%.” Did Tesh report the percent increase
correctly?
Solution: We begin by finding the actual percent increase.
amount of increase
Percent increase 
original amount
13  4 9

  2.25  225%
4
4
The percent increase for PBS was 225%. This is not more than
300%, so Tesh did not report the percent increase correctly.
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