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Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Solving Equations and Inequalities 10 10.1 Solving Equations: The Addition Principle 10.2 Solving Equations: The Multiplication Principle 10.3 Using the Principles Together 10.4 Formulas 10.5 Applications of Percent 10.6 Applications and Problem Solving 10.7 Solving Inequalities 10.8 Applications and Problem Solving with Inequalities Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 2

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas a Evaluate a formula. b Solve a formula for a specified letter. d Use < or > for  to write a true statement in a situation like 6  10. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 3

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas a Evaluate a formula. A formula is a “recipe” for doing a certain type of calculation. Formulas are often given as equations. When we replace the variables in an equation with numbers and calculate the result, we are evaluating the formula. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 4

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas a Evaluate a formula. 2 Socks from Cotton Consider the formula S = 4321x where S is the number of socks of average size that can be produced from x bales of cotton. You see a shipment of 300 bales of cotton taken off a ship. How many socks can be made from the cotton? Source: Country Woman Magazine Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 5

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas a Evaluate a formula. 2 Socks from Cotton Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 6

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas a Evaluate a formula. 3 Distance, Rate, and Time The distance d that a car will travel at a rate, or speed, r in time t is given by d = rt. A car travels at 75 miles per hour (mph) for 4.5 hr. How far will it travel? We substitute 75 for r and 4.5 for t and calculate d: The car will travel 337.5 mi. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 7

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas b Solve a formula for a specified letter. 5 Distance, Rate, and Time Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 8

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas b Solve a formula for a specified letter. 6 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 9

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas b Solve a formula for a specified letter. 7 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 10

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas b Solve a formula for a specified letter. 10 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 11

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas To solve a formula for a given letter, identify the letter and: 1. Multiply on both sides to clear fractions or decimals, if that is needed. 2. Collect like terms on each side, if necessary. 3. Get all terms with the letter to be solved for on one side of the equation and all other terms on the other side. 4. Collect like terms again, if necessary. 5. Solve for the letter in question. b Solve a formula for a specified letter. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 12

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.4 Formulas b Solve a formula for a specified letter. 12 Averages Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 13

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