How to Solve Algebra Problems Step by Step

Solving Algebra word problems is useful in helping you to solve earthly problems.  While the 5 steps of Algebra problem solving are listed below, this article will focus on the first step, Identify the problem.

Use the Following Steps to Solve Word Problems:

1. Identify the problem.
2. Identify what you know.
3. Make a plan.
4. Carryout the plan.
5. Verify that the answer makes sense.

IDENTIFY THE PROBLEM

Back away from the calculator; use your brain first.

 Your mind analyzes, plans, and guides in the labyrinthine quest for the solution. Think of the calculator as merely a tool that makes the journey easier. After all, you wouldn’t want a surgeon to crack your ribs and perform a heart transplant without first identifying the source of your chest pains.

The steps of identifying the problem are:

1. Express the problem question or statement.
2. Identify the unit of the final answer.

STEP 1:  EXPRESS THE PROBLEM QUESTION OR STATEMENT

In Algebra word problems, the problem is expressed as either a question or a statement.

Question:

• How many trees will John have to plant?
• How many televisions will Sara have to sell to earn $50,000?

Statement:

• Find the number of trees John will have to plant.
• Solve for the number of televisions Sara will have to sell to earn $50,000.

STEP 2: IDENTIFY THE UNIT OF THE FINAL ANSWER

What will the answer look like? Now that you understand the word problem’s purpose, determine the answer’s unit.

For example, will the answer be in miles, feet, ounces, pesos, dollars, the number of trees, or a number of televisions?

EXAMPLE 1: ALGEBRA WORD PROBLEM

Javier is making brownies to serve at the family picnic.  If the recipe calls for 2 ½ cups of cocoa to serve 4 people, how many cups will he need if 60 people attend the picnic?

1. Identify the problem:  How many cups will Javier need if 60 people attend the picnic?
2. Identify the unit of the final answer: Cups

EXAMPLE 2: ALGEBRA WORD PROBLEM

In the market for computer batteries, the intersection of the supply and demand functions determines the price, p dollars, and the quantity, q, of goods sold.

Supply function: 80q – p= 0
Demand function: 4q + p= 300

Determine the price and quantity of computer batteries sold when these functions intersect.

1. Identify the problem:  How much will the batteries cost and how much will be sold when supply and demand functions meet?
2. Identify the unit of the final answer: The quantity, or q, will be given in batteries. The price, or p, will be given in dollars.