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3.11 More Expressions and Equation

Learn how to set up and solve word problems involving ratios, percents, compounds, and variables substitution. Practice algebraic expressions for consecutive integers and sum of integers. Solve problems on consecutive odd and even integers, rectangles, and perimeters.

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3.11 More Expressions and Equation

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  1. 3.11 More Expressions and Equation • Goals: To set up and solve word problems

  2. Graphic Organizer for Word Problems • Ratios (Comparison of Units) • Percents (is/of= %/100) • Compound (x + (x+1)) • If there are expressions with more then 1 type of variable we want to try to use substitution to get only one variable

  3. The second math test was worth half as many as the first write an expression for the total number of points on both tests • Let the first test be f • Let the second test be s • f+s = total points • (but we can not have 2 variables!!!) • s =1/2 f (now we can substitute!) • f+1/2f

  4. If “n” is the first integer, write an algebraic expression for the “2nd consecutive integer.” n + 1 Write an algebraic expression for the “3rd consecutive integer.” n + 2 Write an algebraic expression for the sum of three consecutive integers. n + (n + 1) + (n + 2)

  5. Find three consecutive integers whose sum is 90. Let n = first integer n + (n + 1) + (n + 2) = 90 3n + 3 = 90 3n = 87 n = 29 29, 30, and 31

  6. Write an algebraic expression for the “2nd consecutive odd integer.” n + 2 Write an algebraic expression for the “3rd consecutive odd integer.” n + 4 Write an algebraic expression for the sum of three consecutive odd integers. n + (n + 2) + (n + 4)

  7. Find three consecutive even integers whose sum is 42. Let n = first integer n + (n + 2) + (n + 4) = 42 3n + 6 = 42 3n = 36 n = 12 12, 14, and 16

  8. The sum of an integer and three times the next consecutive integer is 51.What is the largest number? Let n = first integer n + 3(n + 1) = 51 4n + 3 = 51 4n = 48 13 n = 12

  9. The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensions • P = 2L + 2W • P=150 • 150 = 2L +2W • L=(W +15) • 150 = 2 (W +15) +2W • 150 = 2W + 30 +2W • 150= 4W +30 • 120 =4W • W=30 cm • L=30 +15 = 45 cm

  10. Homework: Page 160 (2-22) even You do not have to write the word problem down but you do have to write down the: • data, • draw a picture or diagram, • set up the equation • show your work to solve the equation • put the units on your answer

  11. Earn your P.s. D. (Problem Solving Degree) • You are the “interns” and are trying to earn your Ps. D. ( Doctor of Problem Solving Degree) • Diagnose a word problem as a doctor would a patient • The vocabulary is the “Symptoms” that determine how we “Operate” to determine the correct answer. • A “Final Check-Up” ensures the operation was successful.

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