APPLICATIONS Involving percents

• Percent• 63% of homes have

a computer• 5% sales tax

• 15% commission

• Interpretation• 63 out of 100 homes

have a computer• 5 cents in tax is

charged for every 100 cents in merchandise.

• $15 is earned in commission for every $100 sold.

Percents come in a variety of application in day-to-day life. Many

such applications follow the basic percent equation:

amount = (percent)(base)

Example What percent of 60 is 25.2 Step 1: Read the problem

Step 2: Label the variables.Let x represent the unknown percent.

Step 3: Create a verbal model.

What percent of 60 is 25.2

x 60 = 25.2∙

Step 4: Write a mathematical equation.

x 60 = 25.2∙Step 5: Solve the equation

60x = 25.260x = 25.2

60 60

Step 6: Interpret the results and write the answer in words.

x = 0.42, or 42%

Example A new digital camera cost $429.95Compute the sales tax if the tax rate is 4%

Step 1: Read the problem

Step 2: Label the variables.Let x represent the amount of tax.sales tax = (tax rate)(price of merchandise)

Step 3: Create a verbal model.

Step 4: Write a mathematical equation.x = $17.198

x = $17.20Step 5: Solve the equation

Step 6: Interpret the results and write the answer in words.

Sales tax is $17.20The total cost = cost of merchandise + amount of tax$429.95 + $17.20 = $447.15

x = (0.04)($429.95)x = (0.04)($429.95)

Example A video game is purchased for a total of $48.15, including sales tax. If the tax rate is 7%, find the original price of the video game before the sales tax.

Step 1: Read the problem

Step 2: Label the variables.Let x represent the price of the videogame.

(Original) + (Sales) = (total) price tax cost Step 3: Create a verbal model.

Step 4: Write a mathematical equation.

1.07x = 48.15 1.07 1.07

x = 45 Step 5: Solve the equation

Step 6: Interpret the results and write the answer in words.

The original price is $45.00

x + 0.07x = $48.15

1.07x = 48.15

APPLICATIONS INVOLVING SIMPLE INTEREST

( SIMPLE ) = (PRINCIPAL)( ANNUAL )( TIME ) INTEREST INVESTED INTEREST RATE IN YEARS

To find the simple interest earned on $2000 invested at 7.5% interest for 3 years, we have

I = PrtInterest = ($2000)(0.075)(3)

= $450