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How to Solve Algebra Problems Step by Step 3

Make a Plan

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Work with a pencil and a serious eraser. It’s ok to make mistakes. Relax if you haven’t built a perfect problem solving model as quickly as your classmates. Consider the U.S. Constitution, a document designed to answer the question: How will Americans be governed?

 

This controversial document was still a work in progress in its 18th century infancy. The Bill of Rights was an editorial change (ok, a political change to protect We the People from King George-ish tyranny). Problem solving is easier after a few rough drafts. 

Here are the 5 steps to solving any Algebra word problem:

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

This article will focus on Step 3, Make a plan.

Methods of Building Your Plan

  • Write down your plan
  • Talk out your plan
  • Make a table
  • Draw a line, circle, or bar graph
  • Draw any other type of graph
  • Draw a picture (You’re never too old to do this.)
  • Work backward

Example 1: Algebra Word Problem

The Pennrose Theater expects 275 patrons per new movie every weekend.  How many new movies should they show this weekend if they expect 2,200 patrons?

Make a Plan

For every new movie, 275 patrons come to the Pennrose Theater.

1 movie = 275 patrons
2 movies= 275 *2 = 550 patrons
3 movies= 275*3= 825 patrons

275*number of movies = 2,200 patrons or 275*m = 2,200, where m represents the number of movies.

Solve for m to answer the question.

Example 2: Algebra Word Problem

The area of a rectangle is p6q3 square inches.  If the length is p4q2 inches, then what is the width in inches?

Make a Plan

The exercise wants me to find the width, but I only have area and length.
Think: What formula has area, length, and width? Area of a rectangle includes all three!

Arearectangle= length * width
p6q3 = p4q2 * width

Solve for width to answer the question.

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