Section 1.1, Slide 1 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. 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 percents in decimal form: 36% 19.32% Solution:

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 6 Percent Example: Write each of the following decimals as percents: Solution:

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 7 Percent Example: Write each of the following decimals as percents: Solution: 0.29 is 29 hundredths, so 0.29 equals 29% would be 35%, so is 35.4%.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 8 Percent Example: Write as a percent. Solution:

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 9 Percent Example: Write as a percent. Solution: Convert to a decimal. We may write as 37.5%. That is, %.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 10 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 11 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 12 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 13 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 14 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 15 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 16 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 17 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 18 Example: What is 35% of 140? Solution: The Percent Equation

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 19 Example: What is 35% of 140? Solution: The Percent Equation The base is 140 and the percent is 35% = So the amount is 0.35 × 140 = 49.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 20 Example: 63 is 18% of what number? Solution: The Percent Equation

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 21 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 22 Example: 288 is what percent of 640? Solution: The Percent Equation

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 23 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 24 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

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 25 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: = 82 (base) Number of victories: 53 (amount)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 26 Example: In 2006, the average borrower who graduated from a public college owed $17,250 from student loans. This amount was up % from Find the average amount of student loan debt that graduates from these schools owed in The Percent Equation (continued on next slide)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 27 Solution: $17,250 is the amount. 100% of the debt owed in 1996 plus the % increase is the percent. The Percent Equation

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 28 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 29 Solution: Jaye must pay $ % of the amount over $30,650. Taxes

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 30 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 31 Solution: The tax on $30,650 would be $ % of the amount of taxable income over $7,550. Taxes

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 32 Definitions: Inflation is a rise in the level of prices of goods and services over a period of time. Consumer Price Index (CPI) is a measure of inflation obtained by comparing current prices with base prices in Inflation

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 33 Rate of Inflation is measured by: Inflation

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 34 Example: From 2000 to 2009 the CPI of ice cream rose from to Calculate the percent of increase, or rate of inflation, for this item. Inflation

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 35 Example: Consumer Price Index for college tuition for the years 1984 to Inflation In 2009, the overall CPI was 214, which meant that, on the average, prices were 214% of what they were in Use the given graph to compare the rise in tuition at public and private colleges with the CPI. (continued on next slide)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 36 Solution: For public colleges, we will use the percent equation Percent x base = amount, where the base is 971 and the amount is 4,544. Percent x 971 = 4,544 Inflation (continued on next slide)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.1, Slide 37 Solution: For private colleges, the base is 5,315 and the amount is 23,201. In both cases, the rise in college tuition is more than twice the CPI of 214. Inflation