consumer mathematics

Section 1.1, Slide 1

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.


Consumer Mathematics

The Mathematics of Everyday Life

8

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.


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.


Percent

• Example: Write each of the following percents in decimal form:

36% 19.32%

• Solution:


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%.


Percent

• Example: Write as a percent.

• Solution:

Convert to a decimal.

We may write 0.375 as 37.5%. That is, %.


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)


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


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:


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?



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.


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?



Percent of Change

• Solution: Percent or markup is the same thing as percent of change in the base price.


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.


• Example: What is 35% of 140?

• Solution:


The base is 140 and the percent is 35% = 0.35.

So the amount is 0.35 × 140 = 49.


• Example: 63 is 18% of what number?

• Solution:


The percent is 18% = 0.18 and the amount is 63.


• Example: 288 is what percent of 640?

• Solution:


The base is 640 and the amount is 288.


• Example: A basketball team had a record of 53 wins and 29 losses. What percent of their games did they win?

• Solution:


Total number of games: 53 + 29 = 82 (base) Number of victories: 53 (amount)


• 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.




• Solution:

$17,250 is the amount.

100% of the debt owed in 1996 plus the 115.625% increase is the percent.



• Example: If Jaye is unmarried and has a taxable income of $41,458, what is the amount of federal income tax she owes?

Taxes



• Solution: Jaye must pay $4220 + 25% of the amount over $30,650.

Taxes


• Example: How did the IRS arrive at the $4,220 amount in column 3 of line 3?

Taxes



• Solution: The tax on $30,650 would be $755 + 15% of the amount of taxable income over $7,550.

Taxes

consumer mathematics

Documents