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Problem Solving with Formulas: Rectangles, Consecutive Integers, and Literal Equations

This chapter focuses on problem-solving techniques using formulas in geometry and algebra. It covers the dimensions of rectangles, including how to find their length and width using perimeter equations. It also addresses consecutive integers and how to manipulate their sums to find specific numbers. Additionally, the chapter explores literal equations and transforming them to isolate variables, providing a comprehensive understanding of mathematical problem-solving methods. Great for learners looking to enhance their analytical skills!

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Problem Solving with Formulas: Rectangles, Consecutive Integers, and Literal Equations

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  1. Chapter 2 Sections 5-6 Problem Solving and Formulas

  2. Problem Solving • The length of a rectangle is 6 inches more than its width. The perimeter of the rectangle is 24 in. What is the length? P = 2l +2w 24 = 2(w+6) + 2(w) w 24 = 2w + 12 + 2w l = w + 6 24 = 4w + 12 w + 6 l = 3 +6 12 = 4w l = 9 in 3 = w

  3. The width of a rectangle is 2 cm less than its length. The perimeter of the rectangle is 16 cm. What is the length? P = 2l + 2w l – 2 16 = 2l + 2 (l - 2) 16 = 2l + 2l – 4 16 = 4l – 4 l 20 = 4l l = 5 cm

  4. Consecutive Integers-differ by 1. • The sum of three consecutive integers is 147. Find the integers. N + N + 1 + N + 2 = 147 N: first number N+1: second number N +2 : third number 3N + 3 = 147 3N = 144 N = 48 48, 49, 50

  5. The sum of three consecutive integers is 48. • The sum of four consecutive even integers is 60. • The sum of two consecutive odd integers is 44.

  6. Literal Equation- two or more variables • Solve the formula A = ½ bh for height h. • Solve the formula for the perimeter of a rectangle for the width. P = 2(l + w) • Solve the formula V = lwh for w.

  7. Transforming Equations • Solve y = 5x + 7 for x. • Solve z – br = p for b. • Solve y + 2x = 5 for y. • Solve 5x + 4y = 4 for y. • Solve 2x + 7y = 4 for y.

  8. HW # 6 • Page 107 (1, 2, 4, 6 -8) • Page 113 (1-6, 9 -14)

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