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Chapter 6: Problem 61

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

Short Answer

Expert verified
The step-by-step approach to solve algebraic word problems involves understanding the problem, assigning variables to unknown quantities, formulating equations based on the problem, solving the equations, verifying the solutions, and finally interpreting the answer in the context of the problem.

Step by step solution

01

Understand the Problem

Read the problem carefully and numerous times if necessary, to understand what is being asked. Identify and note the known and unknown quantities.
02

Assign Variables

Assign variables to the unknown quantities. Ensure to choose variables that make sense based on the provided problem.
03

Create Equations

Formulate an equation or a set of equations that represent the situation described in the algebraic word problem. Be sure to include all of the known quantities and variables representing unknown quantities.
04

Solve the Equations

Solve the equation or system of equations. This can often involve methods such as substitution or elimination if you're dealing with multiple variables.
05

Check Solution

Verify the solution obtained by substituting calculated values back into the original equation(s). If it is correct, it should make the equation(s) a true statement
06

Interpret the Answer

Finally, translate the mathematical solution back into the context of the problem. Make sure the answer makes sense in relation to the original problem.

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Most popular questions from this chapter

Solve each inequality and graph the solution set on a number line. \(4(x+1)+2 \geq 3 x+6\)

In Exercises 33-36, solve each equation using the zero-product principle. \(x^{2}+8 x+15=0\)

Use the five-step strategy for solving word problems to find the number or numbers described. When a number is decreased by \(20 \%\) of itself, the result is 20 . What is the number?

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In Exercises 39-40, name the property used to go from step to step each time that "(why?)" occurs. $$ \begin{aligned} &7+2(x+9) \\ &=7+(2 x+18) \quad(\text { why? }) \\ &=7+(18+2 x) \quad(\text { why? }) \\ &=(7+18)+2 x \quad(\text { why? }) \\ &=25+2 x \\ &=2 x+25 \quad \text { (why?) } \end{aligned} $$
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