Problem 79 - College Algebra

Question

In your own words, describe a step-by-step approach for solving algebraic word problems.

Step-by-Step Solution

Answer

The general approach to solving algebraic word problems involves understanding the problem, defining the unknowns, setting up the equations, solving these equations and finally, verifying the solutions.

Step 1: Understanding the Problem

The first step involves reading the problem carefully and identifying what the problem is asking for. This step is crucial in figuring out the unknowns, which will be represented as variables in the algebraic equations.

Step 2: Defining the Unknowns

After understanding the problem, assign a variable to represent the quantity that we are trying to find. If there are several unknowns, assign a separate variable for each.

Step 3: Setting Up the Equations

Using the problem's information, set up an equation that describes the relationships between the different unknowns. Every clue in the problem should be incorporated into the equation.

Step 4: Solving the Equations

Solve the equation(s) to find the value of the variables. This could involve methods such as addition, subtraction, multiplication, division, factoring or use of quadratic formula, depending upon the nature of the equations.

Step 5: Verifying the Solutions

The last step is verification. To ensure the obtained solutions make sense in the context of the original problem, substitute the solution back into the original equation to see if it is satisfied.