Introduction to Problem Solving

MATH 018

Combined Algebra

S. Rook

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Overview

• Section 2.4 in the textbook– Solving Word Problems

Solving Word Problems

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Solving Word Problems

• To solve a word problem:– Understand what the problem is asking

• Reread the problem until the question is understood

– Identify the elements of the problem and organize any known information

– Translate the problem into an equation• Look for key words

– Solve the problem• Don’t forget the units – this is a common mistake!

– Check to see if the answer makes sense

• Solving word problems does not come naturally to many people– Practice is the ONLY way to get better!

Setting Up and Solving a Simple Word Problem

• Consider the following: “Three times the sum of a number and six is forty-eight. What is the number?”

• What are we asked to find?

• What are the elements of the problem? Are they related?

• What is the equation that uses those elements?

• What is the solution in the context of the problem?

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Solving Word Problems (Example)

Ex 1: Translate and solve for the number:

a) The sum of three times a number and six is fifteen

b) Twice the difference of a number and two is the same as the sum of four and three times the number

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Setting Up and Solving a More Complicated Word Problem

• Consider the following: “Suppose in a certain parking lot there are only cars & trucks and there are 20 more trucks than cars. If there are 106 vehicles in the lot, find the number of trucks and cars in the parking lot”

• What are we asked to find?• What are the elements of the problem and are

they related?• What is the equation that uses these elements?• What is the solution in the context of the problem?

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Solving Word Problems (Example)

Ex 2: Create an equation and solve for the three integers:

a) The sum of three consecutive odd integers is -2301.

b) The sum of three consecutive integers is 522.

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Solving Word Problems (Example)

Ex 3: In addition to tuition, an HCC student wanting to take a Chemistry class needs to pay a laboratory fee and buy a textbook. For the textbook, the student spends $20 more than three times the cost of the laboratory fees. If the student spent a total of $190, how much did she spend on the textbook and on the laboratory fees?

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Solving Word Problems (Example)

Ex 4: A certain 30 minute news show is divided into three segments: top stories, weather, and sports. The weather segment is 1⁄3 as long as the top stories segment and the sports segment is five minutes less than the top stories segment. How long are each of the segments?

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Solving Word Problems (Example)

Ex 5: Recall that the three angles of a triangle sum to 180°. Two angles of the triangle have the same measure. The third angle measures four times the length of either of the first two angles. What are the angle measures of the triangle?

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Summary

• After studying these slides, you should know how to do the following:– Set up and solve word problems

• Additional Practice– See the list of suggested problems for 2.4

• Next lesson– Formulas and Problem Solving (Section 2.5)