How to Solve Word Problems Involving the One-Step Equation

A step-by-step guide to solving word problems involving the one-step equation

One-step equations are equations that can be solved in a single step. They are equations of the form ax = b or x/a = b, where a and b are numbers and x is the variable we are solving for.

Word problems that involve one-step equations often ask us to solve for a missing variable given some other information.

Here is a step-by-step guide to solving word problems involving one-step equations:

Step 1: Read the problem carefully and identify the unknown variable.

It is important to understand what the problem is asking and what we are trying to find. Identify the variable that is unknown and needs to be solved.

Step 2: Translate the problem into an equation.

Use the given information in the problem to set up an equation that can be solved for the unknown variable. Make sure to use the correct mathematical operation for the given problem. For example, if the problem involves addition, subtraction, multiplication, or division, use the corresponding mathematical symbol to write the equation.

Step 3: Solve the equation.

Solve the equation by isolating the unknown variable on one side of the equation. If the variable is on the left side, move it to the right side by performing the opposite mathematical operation. If the variable is on the right side, move it to the left side by performing the opposite mathematical operation. Perform the same operation on both sides of the equation to maintain balance.

Step 4: Check the solution.

Plug the solution obtained in Step 3 into the original equation and check whether the equation holds true. If the equation holds true, the solution is correct.

Step 5: Write the final answer.

Write the final answer in a sentence or in the appropriate units, depending on what the problem is asking for.

Note that the steps may need to be adapted depending on the specific problem. However, following this guide can help make the process of solving one-step equation word problems more straightforward.

Word Problems Involving the One-Step Equation – Example 1

How many packs of popcorn (p) can you buy for $52 if one package costs $4?
Solution:
List keywords and phrases in the problem to write the equation.
Each package costs $4.
The total money is $52.
How many packs of popcorn is p.
The model is a multiplication equation. \(4.p=52\)
Solve it by the inverse operation. \(4.p=52→p=52÷4=13\)
You can buy 13 packs of popcorn for $52.

Word Problems Involving the One-Step Equation – Example 2

At a restaurant, Maria and her three friends decided to divide the bill evenly. If each person paid $21 then what was the total bill (b)?
Solution:
List keywords and phrases in the problem to write the equation.
There were 4 people.
Each person paid $21.
What was the total bill b.
The model is a division equation. \(\frac{b}{4}=21\)
Solve it by the inverse operation. \(\frac{b}{4}=21→b=21×4=84\)
The total bill was $84.