Problem 47 - Introductory and Intermediate Algebra for College Students 4th

Question

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

Step-by-Step Solution

Answer

The step-by-step approach to solving algebraic word problems involves understanding the problem, defining variables, translating into mathematical expressions, forming equations, solving the equations using algebraic methods, and interpreting the solution in the context of the problem.

Step 1: Understand the Problem

Start off by reading the word problem carefully. Ensure you comprehend the question being asked, the information provided, and what needs to be found. Highlight key details, and write the problem in your own words if it helps.

Step 2: Define the Variables

Identify what you’re solving for and choose a variable to represent that unknown. If there are multiple unknowns, choose variables for each. Make sure to write down what each variable represents.

Step 3: Translate into Mathematical Expressions

Translate the words into mathematical expressions. Words like ‘sum’, ‘difference’, ‘product’, ‘quotient’, ‘increased by’, ‘decreased by’, ‘twice’, ‘half’ etc., indicate mathematical operations. Turn these into the correct mathematical symbols.

Step 4: Form the Equations

Using the mathematical expressions from the previous step, form one or more equations that represent the situation described in the problem.

Step 5: Solve the Equations

Solve the equation or system of equations using algebraic methods. This could involve techniques like combining like terms, using the distributive property, factoring, and so forth.

Step 6: Interpret the Solution

Finally, ensure you interpret the solution in the context of the original problem. Check the solution back into the original problem to ensure it makes sense.