Topic: Linear Equations and Inequalities
Subtopic: Applications of Linear Equations
Overview
Our first set of word problems! Be sure to concentrate on those types listed below. The key is in the translating step when the word problem is translated into an equation. Read the problem carefully, assign variables, know what you are looking to solve, take your time! You can do it if you take one step at a time and not allow yourself to get overwhelmed.
One caution when working with percent problems: remember that percents must be taken of something - so the percent must be multiplied by something. One of the most common errors is to take the percent of the wrong thing. For example, in "A TV is marked up 50% over its wholesale price. It sells for $200, what is the wholesale price?" It is WRONG to take 50% of $200 - that would be 50% of the retail price. Instead start with the unknown wholesale price, x, add the mark-up, 50% of x, to get the retail. I.e., solve x+0.50x=200.
Word problems is often a sticking point for students, but if you keep an optimistic attitude, take one step at a time, and read the problem carefully, you can do it! If you need additional assistance, I recommend a little book: How to Solve Word Problems in Algebra by Mildred Johnson. There are others available that are good too, but this one is easy to follow and full of examples like those we cover in this class.
Objectives
By the end of this topic you should know and be prepared to be tested on:
- 2.3.1 Solve elementary word problems of the following types:
Number problems (including consecutive)
Money problems
Percent problems
Geometry problems including perimeter, area - 2.3.2 Solve triangle problems including those involving the "180° triangle theorem", complementary angles, or supplementary angles
- 2.3.3 Modeling data with a linear equation, i.e. describe an application using a linear equation
Terminology
Define: perimeter, area, complementary, supplementary
Text Notes
Text:
Intro & Inter Algebra for CS 3ed by Blitzer, sect. 2.5-2.6
- ch 2.5 pg 148 has a chart for translating words to algebraic expressions.
- ch 2.5 includes examples of the following application problems: consecutive integers, business apps, geometry, percent/money. Any of these may appear on the quiz!
- ch 2.6 pg 159-160 has the formulas for perimeter and area of four basic 2D shapes. These geometry formulas and their applications are important and may appear on the quiz!
- ch 2.6 pg 162-164 covers volume formulas. I personally think that you have enough to learn without including the volume formulas. You can SKIP the volume formulas, problems involving volume, and examples 4-5 in the text. I will not test you on volume.
- ch 2.6 pg 164-166 covers the angles of a triangle theorem, complementary angles, and supplementary angles. You should cover know these terms and how to solve application problems involving angles and angles in triangles.