Section 8'1 Percent, Sales Tax, and Income Tax

1
Section 8.1Percent, Sales Tax, and Income Tax

• 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
• Divide the numerator by the denominator.
• Multiply the quotient by 100. This is done by
  moving the decimal point in the quotient two
  places to the right.
• Add a percent sign.

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Expressing a Fraction as a Percent

• Example Express as a percent.
• Solution
• Step 1. Divide the numerator by the denominator.
• 5 8 0.625
• Step 2. Multiply the quotient by 100.
• 0.625 x 100 62.5
• Step 3. Add a percent sign.
• 62.5
• Thus, 62.5.

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Expressing a Decimal as a Percent

• To express a decimal as a percent
• Move the decimal point two places to the right.
• Attach a percent sign.
• Example 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
• Move the decimal point two places to the left.
• Remove the percent sign.
• Example Express each percent as a decimal
• 19 b. ¼

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Expressing a Percent as a Decimal NumberExample
Continued

• Solution Use the two steps.
• a.
• Thus, 19 0.19.
• We change the fraction into a decimal, then use
  the steps
• Thus, ¼ 0.0025.

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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 x items cost

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Percent and Sales Tax

• Example Suppose that the local sales tax rate is
  7.5 and you purchase a bicycle for 394.
• How much tax is paid?
• What is the bicycles total cost?
• Solution
• Sales tax amount tax rate x items cost
• The tax paid is 29.55.

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Percent and Sales TaxExample Continued

• The bicycles total cost is the purchase price,
  394, plus the sales tax, 29.55.
• Total Cost 394.00 29.55 423.55
• The bicycles total cost is 423.55.

10
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 price discount rate x original price.
• Example A computer with an original price of
  1460 is on sale at 15 off.
• What is the discount amount?
• What is the computers sale price?

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Percent and Sales PriceExample Continued

• Solution
• Discount amount discount rate x original price
• The discount amount is 219.

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Percent and Sales PriceExample Continued

• A computers sale price is the original price,
  1460, minus the discount amount, 219.
• Sale price 1460 - 219 1241
• The computers sale price is 1241.

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Percent and Income Tax

• Calculating Income Tax
• Determine your adjusted gross income
• Determine your taxable income

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Percent and Income Tax

• Determine the income tax

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Percent and Income Tax

• The table shows tax rates, standard deductions,
  and exceptions for the four filing status
  categories.

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Percent and 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 Women with no dependents Gross income
52,000 Adjustments 4,000 Tax credit 500

• Deductions
• 7500 mortgage interest
• 2200 property taxes
• 2400 charitable contributions
• 1500 medical expenses not covered the
  insurance

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Percent and Income TaxExample Continued

• Solution
• Step 1. Determine the adjusted gross income.
• Adjusted gross income Gross income
  Adjustments
• 52,000 -
  4000
• 48,000

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Percent and Income TaxExample Continued

• Step 2. Determine taxable income.
• We substitute 12,100 for deductions in the
  formula for taxable income.

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Percent and Income TaxExample Continued

• Taxable income Adjusted gross income
  (Exemptions Deductions)
• 48,000 (3200
  12,100)
• 48,000 15,300
• 32,700
• Step 3. Determine the income tax.
• Income tax Tax computation Tax credits
• Tax Computation - 500
• Since the single woman taxable income is 32,700
  she falls in the tax bracket of 25.

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Percent and Income TaxExample Continued

• This means that she owes
• 10 on the first 7300 of her taxable income,
• 15 on her taxable income between 7301 to
  29,700, inclusive,
• and 25 on her taxable income above 29,701.

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Percent and Income TaxExample Continued

• 0.10 x 7300 0.15 x 22,400
  0.25 x 3000
• 730 3360 750
• 4840
• We substitute 4840 for the tax computation in
  the formula for income tax.
• Income tax Tax computation Tax credits
• 4840 - 500
• 4340
• Thus, the income tax owed is 4340.

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Percent and Change

• If a quantity changes, its percent increase or
  its percent decrease can be found as follows
• Find the fraction for the percent increase or
  decrease
• Find the percent increase or decrease by
  expressing the fraction in step 1 as a percent.

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Percent and Change

• Example 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.

• Find the percent increase in world population
  from 2000 to 2150 using the high projection data.
• Find the percent decrease in world population
  form 2000 to 2150 using the low projection data.

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Percent and ChangeExample Continued

• Solution
• Use the data shown on the blue, high-projection,
  graph.
• The projected percent increase in world
  population is 400.

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Percent and ChangeExample Continued

• Use the data shown on the green, low-projection,
  graph.
• The projected percent decrease in world
  population is 33?.

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Abuses of Percents

• Example 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 Test report the
  percent increase correctly?
• Solution We begin by finding the actual percent
  increase.
• The percent increase for PBS was 225. This is
  not more than 300, so Tesh did not report the
  percent increase correctly.