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 integers)

Money problems

Percent problems

Some basic business applications

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**

Terms you should be able to define: perimeter, area, vertex, angle, complementary, supplementary

**Text Notes**

You must know how to use the perimeter and area formulae for basic 2D shapes. However you can SKIP the 3D shapes. You will not be tested on volume nor surface area of 3D shapes in this level course.

**Supplementary Resources**

Looking for a sheet with all the geometry formulae? Maryland K12: Geometry Reference Sheet is a good (and printable) option. Remember though that we are only covering the 2D plane shapes not the 3D solid shapes.

For extra examples of basic word problems I recommend PurpleMath.com. Go to the lessons at www.purplemath.com/modules, scroll down to the "Solving Word Problems" section. There you will find links to "number" problems, "coin" (money) problems, "percent of" problems, and "area/volume/perimeter" (geometry) problems.