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Martin-Gay, Beginning Algebra, 5ed 22

Strategy for Problem Solving

General Strategy for Problem Solving

1 Introduction: Understand the problem by:• Read and reread the problem• Choose a variable to represent the unknown• Construct a drawing, whenever possible

2. Body: Translate the problem into an equation

and solve the equation

3. Conclusion: Interpret your result• State your conclusion

Page 3: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 33

Page 4: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 44

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Martin-Gay, Beginning Algebra, 5ed 55

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Page 7: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 77

Page 8: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 88

Find the area of the trapezoid.

Find the volume of the right circular cylinder.

Page 9: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 99

Page 10: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 1010

It is often necessary to rewrite a formula so that it is solved for one of the variables.

This is accomplished by isolating the designated variable on one side of the equal sign.

Page 11: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 1111

Example

mnrT

mnr

T Divide both sides by mr.

nmr

T Simplify right side.

Solve for n.

Page 12: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 1212

Solving Equations for a Specific Variable1. Multiply to clear fractions.

2. Use distributive property to remove grouping symbols.

3. Combine like terms to simplify each side.

4. Get all terms containing specified variable on the same side, other terms on the opposite side.

5. Isolate the specified variable.

Page 13: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 1313

ExampleSolve for T.

PRTPPPA Subtract P from both sides.

PRTPA Simplify right side.

PRT

Divide both sides by PR.

TPR

Simplify right side.

A P PRT

Page 14: Martin-Gay, Beginning Algebra, 5ed 22 Strategy for Problem Solving General Strategy for Problem Solving 1Introduction: Understand the problem by: Read

Martin-Gay, Beginning Algebra, 5ed 1414

Solve for the indicated variable.

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