2.2 Sub Chapter Notes

An Introduction to Solving Word Problems • Working a word problem requires both the mathematical skills and the ability to restate the facts as variables in equations. • Word Problem Solving Process: 1. Determine the facts 2. Define the variables 3. Create an equation 4. Solve the equation 5. Check your answer Working a word problem is first of all a translation process. You must: 1. Determine your facts. 2. Define the variables. 3. Create an equation. Only then do you perform the steps to solve for the requested information.

Working a word problem requires that you read carefully and think about what the words are telling you. Constantly think about what the problem is telling you. Stick very closely to the facts as presented. Separate the facts. You might want to make a list. Note what is being asked for so you can define your variables. Also note any stray information that you will not use. Many word problems include information that is interesting but not needed to solve for the requested answers.

Finding Perimeter • Word Problems require translation from English, or some language, into math numbers and symbols. • Formula: a generalized equation for a characteristic or action that works in every situation of its kind. You use a formula by choosing it for the situation you have and then substituting into the formula the specific facts of your situation, and solving for what you need to know. • Always check when you’re done to be sure: 1. You have every answer asked for in the problem. 2. The answer works with the facts in the problem. • The most important part of working with any word problem is the translation process that creates the equation you will work with. Read the words carefully. Draw a sketch. Write out the facts you know and what you are being asked to find. Now take all those facts and convert them into an equation using the formula that you’ve decided on.

www.thinkwell.com

© Thinkwell Corp.

1

Solve the equation for the variable. Are you done? Is the value for w all you need? Check it out to be sure.

Solving a Linear Geometry Problem • A right circular cylinder is the shape of a can of food. It has round tops and bottoms that are the same size. The height forms a right angle with the top and bottom. • The volume of a right cylinder can be found using V = π r 2h. Define the variables: h = the height of the cylinder. r = the distance from the center of the top or bottom to its edge.

In this problem, the radius squared is 36, so our volume formula becomes π times 36 times h.

The height (h) will be found by dividing both sides by 36π. In this case, the height is 4 inches.

Solving for Constant Velocity • A constant velocity problem involves travel at a steady speed. Use the formula d = rt to write an equation for each person. Arsenio's speed is 540 mi/h, but his distance and time are unknown. Therefore, the equation for Arsenio's distance equation is d = 540t. MC Plier's speed is also known: it is 660 mi/h. MC Plier's distance and time are unknown. However, it is known that MC Plier's time is equal to 1 less than Arsenio's time since MC Plier left one hour after Arsenio. So, if Arsenio's time is t, then MC Plier's time is t – 1. And, if Arsenio's distance is d, then MC Plier's distance is 1800 – d. Thus, MC Plier's equation is 1800 − d = 660(t − 1). Substitute the expression 540t into MC Plier's equation for d and solve to find the amount of time that Arsenio traveled before passing MC Plier.

2

© Thinkwell Corp.

www.thinkwell.com