consumer mathematics
Post on 03-Jan-2016
35 Views
Preview:
DESCRIPTION
TRANSCRIPT
Section 1.1, Slide 1
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 8.1, Slide 1
Consumer Mathematics
The Mathematics of Everyday Life
8
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 8.1, Slide 2
Percents, Taxes, and Inflation
8.1
• Understand how to calculate with percent.
• Use percents to represent change.
• Apply the percent equation to solve applied problems.
• Use percent in calculating income taxes.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 3
Percent
The word percent is derived from the Latin “per centum,” which means “per hundred.” Therefore, 17% means “seventeen per hundred.” We can write 17% as or in decimal form as 0.17.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 4
Percent
• Example: Write each of the following percents in decimal form:
36% 19.32%
• Solution:
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 5
Percent
• Example: Write each of the following decimals as percents:
0.29 0.354• Solution:0.29 is 29 hundredths, so 0.29 equals 29%.
0.35 would be 35%, so 0.354 is 35.4%.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 6
Percent
• Example: Write as a percent.
• Solution:
Convert to a decimal.
We may write 0.375 as 37.5%. That is, %.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 7
Percent of Change
• Example: In 1970 the U.S. government spent $82 billion for defense at a time when the federal budget was $196 billion. In 2007, spending for defense was $495 billion and the budget was $2,472 billion. What percent of the federal budget was spent for defense in 1970? In 2007?
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 8
Percent of Change
• Solution:
In 1970, $82 billion out of $196 billion was spent for defense, or
In 2007, $495 billion out of $2472 billion was spent for defense, or
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 9
Percent of Change
The percent of change is always in relationship to a previous, or base amount.
We then compare a new amount with the base amount as follows:
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 10
Percent of Change
• Example: This year the tuition at a university was $7,965, and for next year, the tuition increased to $8,435. What is the percent of increase in tuition?
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 11
Percent of Change
• Solution: The base amount is $7,965 and the new amount is $8,435.
The tuition will increase almost 6% from this year to the next.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 12
Percent of Change
• Example: TV ads proclaim that all cars at a dealership are sold at 5% markup over the dealer’s cost. A certain car is on sale for $18,970. You find out that this particular model has a dealer cost of $17,500. Are the TV ads being honest?
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 13
Percent of Change
• Solution: Percent or markup is the same thing as percent of change in the base price.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 14
The Percent Equation
Many examples with percents involve taking some percent of a base quantity and setting it equal to an amount. We can write this as the equation
This is called the percent equation.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 15
• Example: What is 35% of 140?
• Solution:
The Percent Equation
The base is 140 and the percent is 35% = 0.35.
So the amount is 0.35 × 140 = 49.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 16
• Example: 63 is 18% of what number?
• Solution:
The Percent Equation
The percent is 18% = 0.18 and the amount is 63.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 17
• Example: 288 is what percent of 640?
• Solution:
The Percent Equation
The base is 640 and the amount is 288.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 18
• Example: A basketball team had a record of 53 wins and 29 losses. What percent of their games did they win?
• Solution:
The Percent Equation
Total number of games: 53 + 29 = 82 (base) Number of victories: 53 (amount)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 19
• Example: In 2006, the average borrower who graduated from a public college owed $17,250 from student loans. This amount was up 115.625% from 1996. Find the average amount of student loan debt that graduates from these schools owed in 1996.
The Percent Equation
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 20
• Solution:
$17,250 is the amount.
100% of the debt owed in 1996 plus the 115.625% increase is the percent.
The Percent Equation
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 21
• Example: If Jaye is unmarried and has a taxable income of $41,458, what is the amount of federal income tax she owes?
Taxes
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 22
• Solution: Jaye must pay $4220 + 25% of the amount over $30,650.
Taxes
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 23
• Example: How did the IRS arrive at the $4,220 amount in column 3 of line 3?
Taxes
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.1, Slide 24
• Solution: The tax on $30,650 would be $755 + 15% of the amount of taxable income over $7,550.
Taxes
top related