How to Match Word Problems with the One-Step Equations?

The process involves analyzing the problem, identifying the unknown variable, setting up the equation, solving for the variable, and checking the solution to ensure its validity.

By mastering these techniques, you will be equipped to confidently tackle any matching word problem involving one-step equations that you may encounter.

A step-by-step guide to matching word problems with the one-step equation

One-step equations are considered algebraic equations that require just a single step to be solved.
Word problems are used to know the concept of one-step equations better.

Here’s a step-by-step guide to matching word problems with one-step equations:

Step 1: Read and understand the problem

Read the problem carefully and make sure you understand what it is asking. Identify the key information and variables involved. For example, if the problem states, “A pizza costs \($10\) and the delivery fee is \($3\). How much will two pizzas and delivery cost?” Then, the variables are the cost of one pizza and the cost of delivery.

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Step 2: Identify the unknown variable

Determine the unknown variable that needs to be solved. In the example above, the unknown variable is the total cost of two pizzas and delivery.

Step 3: Write the equation

Translate the problem into an equation. A one-step equation will involve using one operation to isolate the variable. In the example above, you can write the equation as \(2(10) + 3 = x\), where \(x\) is the total cost of two pizzas and delivery. This is because the cost of two pizzas is \(2(10)\), and the delivery fee is \($3\).

Step 4: Solve the equation

Solve the equation to determine the value of the unknown variable. In the example above, you can simplify the equation to \(23 = x\), which means the total cost of two pizzas and delivery is \($23\).

Step 5: Check the solution

Check the solution to ensure its validity. This involves substituting the value of the unknown variable back into the original problem to verify that it makes sense. In the example above, you can check the solution by confirming that two pizzas at \($10\) each plus a \($3\) delivery fee do indeed equal \($23\).

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Step 6: Interpret the solution

Interpret the solution in the context of the problem. In the example above, the solution means that it will cost \($23\) to order two pizzas and have them delivered.

Matching Word Problem with the One-Step Equation – Example 1

How many packages of corn flex can you buy for \($15\) if one package costs \($3\)? Write the equation for it, then solve it.
Solution:
Look for keywords and phrases in the problem to write the equation.
The total money is \(15\) dollars.
The cost of each package of corn flex is \(3\) dollars.
How many packages of corn flex can buy is \(x\).
The model is a multiplication equation: \(3x=15\).
Solve it by the inverse operation. \(3x=15→x=15÷3=5\)
For \(15\) dollars you can buy \(5\) packages of corn flex.

Matching Word Problem with the One-Step Equation – Example 2

After using \(6\) carrots for soup, Meg has \(11\) carrots in the basket. How many carrots did she have before using the soup?
Solution:
Look for keywords and phrases in the problem to write the equation.
She used \(6\) carrots and still had \(11\) carrots.
The total number of carrots is \(x\).
The model is a subtraction equation. \(x-6=11\)
Solve it by the inverse operation. \(x-6=11→x=11+6=17\)
So, she had \(17\) carrots before using the soup.