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How to Solve Algebra Word Problems in 5 Steps

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For solving Algebra word problems you need to use your logic and find out answers for the problem. Here are 5 steps that help you solve Algebra problems with ease

  1. Identify the problem
  2. Identify what you know
  3. Make a plan
  4. Carry out the plan
  5. Verify whether your answer makes sense

Step 1

Identify the problem

The steps for identifying the problem are

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

You find Algebra word problems in the form of a question or statement.

Examples:

Question How many saplings Brown needs to plant? How many televisions Brenda needs to sell to earn $20000?

Statement Find the number of saplings Brown has to plant. Solve for the number of televisions Brenda has to sell to earn $20000.

  • Identify the final unit of the answer

After understanding the purpose of the word problem, try to find out in what unit the answer will be like miles, ounces, pesos, number of trees or number of televisions.

Example for step1

Christiana is making brownies to serve at the family picnic. If the recipe calls for 21/2 cups of cocoa to serve 4 people, how many cups will she need for 60 people who attend the picnic?

  • Identify the problem: how many cups Christiana needs if 60 people attend the picnic?
  • Identify the final unit of answer: Cups

 Step 2

Identify what you know

I need more information What information you have is not adequate and you need more information.

Example for step 2 

Sarah is carpeting a rectangular room in her house. The length of the room is(x+2) feet and the breadth of the room is (x-6) feet and the area of the room is 84 square feet. Find the length and width of the room. Identify what you know

  • Sarah is carpeting a rectangular room
  • The length of the room is x+2
  • The breadth of the room is x-6
  • The area of the room is 84 square feet.
  • The formula for the area of a rectangle is A=lw
  • I need to find x to find the length and breadth of the room.

Step 3

Make a plan

Methods of building your plan

  • Write down your plan
  • Talk about your plan
  • Make a table
  • Draw a bar graph, line or circle
  • Draw any other type of graph
  • Draw a picture

Example for step 3

The Damsels Theater expects 275 patrons every weekend per new movie. How many new movies they will show if they expect 2200 patrons this week end?

  • For every new movie, 275 patrons come to Damsels Theater
  • 1 movie     =275 patrons
  • 2movies =275*2=550 patrons
  • 3 movies=275*3=825 patrons
  • 275*number of movies=2200 or 275*m=2200(m represents the number of movies)
  • Solve for m to find the answer

Step 4

Carry out the plan

Verify whether the plan is sensible. Check whether you have not missed anything or did not approach the problem in the wrong manner.

Example for step 4

Ben and Jack run a combined distance of 28 miles. Ben runs three times as many miles as Jack. How many miles does Jack run?

The plan

  • B+J=28 where B represents the number of miles run by Ben and J represents the miles run by Jack.
  • B=3*J because Ben runs three times as many miles as Jack.
  • Replace B with 3*J in the equation B+J=28

Carry out the plan

  • 3*J+J=28
  • 4*J=28
  • Solve for J: J=7

Step 5

Verify whether your answer makes sense

In the last step you have two red flags that signal wrong answers

  • Your answer is too big or too small
  • The question remains unanswered

Example for step 5

John is driving from his house to his company. On Monday morning John drives 6 miles north on Peter’s road. Then he drives 8 miles east on Willie’s Road to reach his company. On Tuesday morning, John avoids Peter’s and Willie’s Roads. What is the difference between the number of miles John drives on Monday and Tuesday mornings?

John’s drive to his company resembles a right triangle. You can use Pythagorean Theorem.geometry10 miles is the answer

Verify whether your answer makes sense

No. The answer is the direct distance between John’s company and house. It is not the answer for the question what is the difference between the number of miles John drives on Monday and Tues day mornings?

Make a new plan

  • Find the direct distance
  • Add 6 miles and 8 miles to find the total distance traveled on Peter’s and Willie’s Roads
  • Find the difference between the numbers in steps 1 and 2
  • Distance between the company and house is 10 miles
  • Distance traveled on Peter’s and Willie’s Roads is 6+8=14miles
  • Difference between the numbers 14-10= 4 miles

The answer is correct as per arithmetic and it makes sense.

Doing Algebra word problems through step by step approach is logical easy and fun.

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