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Example 2-4b Objective Solve problems by using the percent equation

Example 2-4b Vocabulary Percent equation An equation that describes the relationship between the part, total, and percent Part = percent  total

Lesson 2 Contents Example 1Find the Part Example 2Find the Percent Example 3Find the Total Example 4Apply the Percent Equation

Example 2-1a What number is 46% of 200? Answer: x = 92 Translate from English to Algebra Multiply x= Convert % to decimal 0.46  200 x = 92 1/4

Example 2-1b What number is 72% of 500? Answer: x = 360 1/4

Example 2-2a 26 is what percent of 32? Do inverse on both sides of the equal sign Translate from English to algebra 26 x= 32  Solve for x Ask “what is being done to the variable?” The variable is being multiplied by 32 2/4

Example 2-2a 26 is what percent of 32? Bring down 26 = 32x Answer: 26 x= 32  x /4 Using the fraction bar, divide both sides by 32 Combine “like” terms = 1  x Use the Identity Property to multiply 1  x = x Variable defined as “What Percent” so multiply by Add percent sign % % = x

Example 2-2d 18 is what percent of 80? Answer: x = 22.5% 2/4

Example 2-3a 12 is 40% of what number? Translate from English to algebra 12= 0.40  x Ask “what is being done to the variable?” 3/4 Solve for x The variable is being multiplied by 0.40 Do inverse on both sides of the equal sign

Example 2-3a 12 is 40% of what number? Answer: 12= 0.40  x x 30 3/4 Bring down 12 = 0.40  x Using the fraction bar, divide both sides by 0.40 Combine “like” terms = 1  x Use the Identity Property to multiply 1  x 30 = x

Example 2-3b 36 is 90% of what number? Answer: 40 = x 3/4

Example 2-4a TELEVISIONS In the year 2000, million homes in the United States had at least one television. Of these, 86% also had VCRs. How many homes had VCRs? Words Variable Equation 86% of 102,200,000 is what number? Let x represent number of homes with VCRs 0.86  102,200,000=x 4/4

Example 2-4a Variable is already by itself Multiply Answer: 0.86  102,200,000 = x 87,892,000 = x 4/4 How many homes had VCRs? Add dimensional analysis 87,892,000 homes with VCRs

Example 2-4b COLLEGE A local college has an enrollment of 25,700 students. Of these students, 22% are from out of state. How many of the students are from out-of- state? Answer: 5,654 students from out-of-state * 4/4

End of Lesson 2 Assignment Lesson 8:2Algebra: The Percent Equation All