Department of Mathematics --- College of Science --- University of Utah

Mathematics 1010 online

Word Problems

The reason why so much mathematics is required of students in virtually all disciplines is that mathematics is capable of solving problems arising in those disciplines. Students usually dread word problems because there is an additional layer of complexity: you have to translate the words into mathematics before you can solve the problem. However, you will never be able to solve word problems if you don't try, and keep it in mind that mathematics is the only subject where some problems are not word problems.

Word problems in a class like this are necessarily simple. The information you need to translate them into mathematical problems is either given as part of the word problem, or it is part of a general body of information that should be known by anybody taking this class. Sometimes part of the exercise is to obtain certain information, like a certain formula, or some data, and in that case the required information is usually widely available and can be found in the textbook, in a dictionary, or in an encyclopedia. Becoming resourceful in terms of obtaining information is one of the skills you acquire in this class.

By the nature of word problems there is no general sure fire approach that will solve all of them. However, here are some suggestions:

  1. Draw a picture.
  2. Give names (i.e., assign variables) to the quantities involved. Clearly keep in mind which of the quantities are known, and which you want to know.
  3. Using your variables, translate the statements in the problem into equations (often just one equation).
  4. Solve the equation.
  5. Find similar problems in your textbook and see how they have been solved.
  6. Go back to similar problems you have already solved in this course.
  7. If you cannot solve the problem right away, do not give up. Problem solving takes time and effort, that's just the way it is. Think about the problem, return to it, do some research, talk with friends or tutors, make assumptions and see what their implications are, and continue the process until you are done.
  8. Always Have Expectations
  9. Always Check Your Answers