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Section 1.6 Using Equations to Solve Problems

Section 1.6 Using Equations to Solve Problems. A Problem Solving Strategy Translating Words into an Equation Analyzing a Problem Number-Value Problems Geometry Problems Using Formulas to Solve Problems. Strategy for Word Problems.

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Section 1.6 Using Equations to Solve Problems

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  1. Section 1.6Using Equations to Solve Problems • A Problem Solving Strategy • Translating Words into an Equation • Analyzing a Problem • Number-Value Problems • Geometry Problems • Using Formulas to Solve Problems

  2. Strategy for Word Problems Sally has $5 more than Zeno. Together they have $12. How much does each have? • Analyze the problem: • Read the problem, ask “what do I need to find?”If there’s only one thing, make this your variable.If there are more than one unknown, make one unknown the variable, and put the others in its terms • State the conclusion (without the number) • Choose a meaningful variable (w for Width, etc) • Form an equation using key words or formulas • Substitute numbers and variables in the equation • Solve the equation • State the conclusion (with the number) • Check solution

  3. Translations • Translations rely on translating key words into algebraic symbols to form the equation. 16. FILMS As of December, 2000, Denzel Washington’s top three grossing films, The Pelican Brief, Crimson Tide, and Philadelphia, had earned $269.6 million. If Crimson Tide earned $14 million more than Philadelphia, and if The Pelican Brief earned $9.4 million more than Crimson Tide, how much did each film earn as of that date?

  4. Number-Value Problems Some problems deal with quantities that have a value. In these problems, we must distinguish between the number of and the value of the unknown quantity. For problems such as these, we will use the relationship Number value = total value 22. ASSETS OF A PENSION FUND A pension fund owns 2,000 fewer shares in mutual stock funds than mutual bond funds. Currently, the stock funds sell for $12 per share, and the bond funds sell for $15 per share. How many shares of each does the pension fund own if the value of the securities is $165,000?

  5. Geometric and Formula Problems • These types of problems rely on formulas from geometry. Figure 1-14 p. 65

  6. Formulas are used to set up equations for numeric substitution to solve 36. HEIGHT OF A TRIANGLE If the height of a triangle with a base of 8 inches is tripled, its area is increased by 96 square inches. Find the height of the triangle.

  7. What Next? • Review 1.6 Vocabulary & Concepts • Examine the Grading Matrix • Posted in Class, Also on the Class Website • Present Section 1.7 More Applications

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