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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9 Equations, Inequalities and Problem Solving

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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 9.5 Formulas and Problem Solving

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Martin-Gay, Developmental Mathematics, 2e 33 Formulas A formula is an equation that states a known relationship among multiple quantities (has more than one variable in it) A = lw (Area of a rectangle = length · width) I = PRT (Simple Interest = Principal · Rate · Time) P = a + b + c ( Perimeter of a triangle = side a + side b + side c) d = rt (distance = rate · time) V = lwh (Volume of a rectangular solid = length · width · height) Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

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Martin-Gay, Developmental Mathematics, 2e 44 Example A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 30 feet more than the length of the shortest side. Find the dimensions if the perimeter is 102 feet. The formula for the perimeter of a triangle is P = a + b + c. If we let x = the length of the shortest side, then 2x = the length of the second side, and x + 30 = the length of the third side continued Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

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Martin-Gay, Developmental Mathematics, 2e 55 Formula: P = a + b + c Substitute: 102 = x + 2x + x + 30 102 = x + 2x + x + 30 102 = 4x + 30 102 – 30 = 4x + 30 – 30 72 = 4x 18 = x continued Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

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Martin-Gay, Developmental Mathematics, 2e 66 Check: If the shortest side of the triangle is 18 feet, then the second side is 2(18) = 36 feet, and the third side is 18 + 30 = 48 feet. This gives a perimeter of P = 18 + 36 + 48 = 102 feet, the correct perimeter. State: The three sides of the triangle have a length of 18 feet, 36 feet, and 48 feet. continued Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

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Martin-Gay, Developmental Mathematics, 2e 77 Solving a Formula for a Variable It is often necessary to rewrite a formula so that it is solved for one of the variables. To solve a formula or an equation for a specified variable, we use the same steps as for solving a linear equation except that we treat the specified variable as the only variable in the equation. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

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Martin-Gay, Developmental Mathematics, 2e 88 Step 1:Multiply on both sides to clear the equation of fractions if they appear. Step 2:Use the distributive property to remove parentheses if they appear. Step 3:Simplify each side of the equation by combining like terms. Step 4:Get all terms containing the specified variable on one side and all other terms on the other side by using the addition property of equality. Step 5:Get the specified variable alone by using the multiplication property of equality. Solving Equations for a Specified Varia ble

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Martin-Gay, Developmental Mathematics, 2e 99 Example Solve T = mnr for n. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

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Martin-Gay, Developmental Mathematics, 2e 10 Example Solve for A = PRT for T. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

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Martin-Gay, Developmental Mathematics, 2e 11 Example Solve Factor out P on the right side. Divide both sides by 1 + RT.Simplify. for P. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

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