MJ2A Ch 6.7 – Percent Equation

Bellwork Use the percent proportion to find the missing term 128 is what percent of 640? 12 is 80% of what number? What is 20% of 35?

Assignment Review Text p. 291 #7 – 22

Before we begin… Please take out your notebook and get ready to work… In today’s lesson we will extend what we learned about the percent proportion by looking at a variation of the percent proportion called the percent equation

Objective 6.7 Students will solve percent problems using the percent equation.

Percent Equation The percent equation is a variation of the percent proportion. The big difference is that the percent is expressed as a decimal… The percent equation Part = Percent ∙ Base Lets see what this looks like…

Example 1 Find 52% of 85 First convert 52% to a decimal (0.52) You know that 85 is the base You need to find the part (n) Then write the formula, substitute and do the math. Part = Percent ∙ Base n = 0.52(85) n = 44.2 Therefore, 52% of 85 is 44.2

Example 2 28 is what percent of 70? You know that the base is 70 and the part is 28. Let p = percent Write the formula, substitute, and do the math Part = Percent ∙ Base 28 = p(70) 70 70 0.4 = p Convert the decimal to a percent 0.4 = 40% Therefore, 28 is 40% of 70

Example 3 18 is 45% of what number? You know that the part is 18 and the percent is 45% (0.45). Let b represent the base Write the formula, substitute, & do the math Part = Percent ∙ Base 18 = 0.45(b) 0.45 0.45 40 = b Therefore, 18 is 45% of 40

Your Turn In the notes section of your notebook write the sentence and then find the missing part using the percent equation. 15 is what percent of 60? What is 20% of 110? 30 is 60% of what number?

Discount You can use the percent equation to calculate discount. Discount is the amount by which a regular price is reduced Be careful here…sometimes the question will ask for the discount amount (Which is the original amount times the percent of discount) Some times it will ask you for the sale price (which is the original price less discount) Let’s look at an example

Example Mateo wants to buy a skateboard. The regular price of the skateboard is $135. The skateboard is on sale at a 25% discount. What is the sale price? In this instance they are looking for the sale price…this means you have to calculate discount first and then subtract it from the original price to get the sale price! We can use the percent equation here to find 25% (0.25)of 135 Part = Percent ∙ Base d = 0.25(135) d = 33.75 The discount amount is $33.75. Therefore, the sale price is $101.25 ($135.00 – $33.75 = $101.25)

Your Turn In the notes section of your notebook calculate the discount and sale price of the following: 1. The regular price of a ring is $495. It is on sale for 20% discount. What is the sale price of the ring?

Simple Interest Interest is the amount of money paid or earned for the use of money… To calculate simple interest use the following formula I = prt Where I = interest p = principal r = rate t = time

Simple Interest Since we use a formula for simple interest you are to use the formula method when calculating simple interest The formula method is Write the formula Substitute Do the math.

Example Sandra invests $500 at 5.5% interest. In 2 years how much will she earn? In this instance $500 represents the principal, 0.055 represents the rate, and time is 2 years. I = prt I = 500(0.055)(2) I = 500(0.11) I = 55 Sandra will earn $55.00 interest for investing her money

Comments When working with the simple interest formula you need to know that time is expressed in years. That means if you have less than a year or time not equal to even amounts of years you need to convert the time into years. Example: 3 months would be 3/12 of a year or .25 of a year 20 months would be 20/12 of a year or 1.7 of a year

Your Turn In the notes section of your notebook use the simple interest formula to calculate the interest. 1. Ricardo borrows $250 at 9% interest for six months. How much interest will he pay?

Summary In the notes section of your notebook summarize the key concepts covered in today’s lesson Today we discussed The percent equation – what is it? Discount Simple Interest

Assignment Text p. 301 # 20 – 40 Reminder: This assignment is due tomorrow I do not accept late assignments You do not have to write the sentences. However, you must show how you got your answer (no work = no credit)