Consumer Mathematics

8 Consumer Mathematics The Mathematics of Everyday Life

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.

Percent The word percentis 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? (continued on next slide)

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? (continued on next slide)

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.

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.

The Percent Equation • Example: 63 is 18% of what number? • Solution: The percent is 18% = 0.18 and the amount is 63.

The Percent Equation • Example: 288 is what percent of 640? • Solution: The base is 640 and the amount is 288.

The Percent Equation • 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)

The Percent Equation • 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. (continued on next slide)

The Percent Equation • Solution: • $17,250 is the amount. • 100% of the debt owed in 1996 plus the 115.625% increase is the percent.

Taxes • Example: If Jaye is unmarried and has a taxable income of $41,458, what is the amount of federal income tax she owes? (continued on next slide)

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? (continued on next slide)

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

Consumer Mathematics