Translating Problems into Equations (Level

1) In this video we are going to learn how to

translate simple word problems into equations. Word problems are perhaps one of the most

feared and hated problems encountered in a typical mathematics course, this is due to

a variety of reasons, many students don’t bother reading word problems and if they do

happen to read them they have a hard time understand them. The best strategy to tackle

on word problems head on is by having a plan and sticking to it.

In general, word problems describe a situation in which certain numbers are related to each

other. For the most part some of these numbers are given in the problem and are considered

to be known numbers or quantities. Then you have other numbers for which you have no idea

what their values are these numbers are referred to as your unknowns. You must determine their

value by using the facts of the problem. In this video we will practice translating

simple word problems that contain two facts involving two unknowns. The following steps

will serve as a blue print to get you started in learning how to translate word problems

into equations. In a much later video we will learn how to find the solution of these word

problems by actually solving the equation. For now we first need to learn how to translate

the word problem into an equation. The following three steps will serve as a

guideline for you to practice translating problems into equations.

Step 1: Read the problem carefully. (Whenever you see a word problem just start reading

it so you can get an idea of what the problem is about.

Decide what the unknowns are. (Try to figure out what quantities you need to solve for

or try to figure out for which quantities you have little to no information on. This

is usually a tell tell sign that the quantity is an unknown).

Decide what the facts are. (These facts are key in determining how you will relate the

quantities with each other). Step 2: Choose a variable to represent the

unknowns. Choose a variable for one unknown. (Remember

that you can choose any letter of the alphabet to represent this unknown. Choose letters

that are relevant to the problem like the first letter of a person’s name or object

for example you can use the variable N to represent the name Newton or the variable

L to represent the length of a rectangle, or you can just use the letter x to represent

your unknown. Write an expression for the other unknown

using the variable and one of the facts. (In these problems you will have two unknowns

as a result you need to figure out how the two variables are related to each other and

denote them mathematically by using mathematical operations such as addition, subtraction,

multiplication, and division). Step 3: Reread the problem and write an equation.

(I cannot over emphasize the importance of reading the problem over and over again to

make sure you understand all the facts and how they are related to each other). Once

you understand the facts go ahead and use the facts from the problem to write an

equation. Alright, let’s go over some examples and

illustrate how to use these 3 steps. Translate the problem into an equation.

Maria has twice as much money as Helena. Together they have $36.

Alright, step 1 is to read the problem carefully and determine the unknowns and the facts.

The facts of this problem are represented by the numbered sentences. Notice that in

this problem the unknowns are the amount of money that Maria and Helena each have, since

we are not explicitly told how much money they have in their possession. Rather we are

given a relationship of this amount between the two persons. This relationship will be

used in step 2. In step two we go ahead and assign variables to our unknowns. Many students

have a hard time with this step, so let’s focus on this step, we already know that our

unknowns represent the amount of money that Maria and Helena have. The question we should

ask our self’s is how do we algebraically denote them with a variable. From the first

sentence we know that Maria has twice as much money as Helena. We are actually given some

kind of relation between Maria’s amount and Helena’s amount, this is not the case

for the amount of money that Helena has. As a rule of thumb you should always assign the

first variable to the quantity for which you have the least amount of information. In this

case we really don’t know much about Helena’s amount so let’s go ahead and assign this

quantity with the letter h, now if we use this variable along with the first sentence

we can represent Maria’s amount as 2h for twice as much. All we need to do now

is to write an equation relating these two expressions. Notice that in sentence 2 we

are told that together Maria and Helena have $36. This means that if we were to add the

amount of money that Maria and Helena have they would add up to $36. So our equation

becomes h + 2h=36 and this is our final answer. We have successfully translated the

word problem into an equation. In a later video we will learn how to solve this equation,

for now we want to practice using these 3 steps which provide the framework needed so

you can tackle these and future word problems. Alright, let’s try the next example. A piece of wood 50 inches long is sawed into

two pieces. One piece is 5 inches longer than the other. If a word problem involves lengths or distances,

a sketch can help you visualize and analyze the problem. So feel free to use your artistic

skills when solving word problems. Alright let’s start with step 1: we first

need to identify our unknowns, we need to figure out for which quantities we have limited

or no information. In this case we really don’t know how much each of the individual

pieces measure so our unknowns are the lengths of these two pieces of wood.

Step 2: Next we need to assign variables to our unknowns, before we do this we need to

first assign a variable to the unknown that contains the least amount of information.

From sentence 2 we are told that one piece is 5 inches longer than the other piece. This

means that we have one piece that is larger than the other piece. We have a small

and a large piece. Looking at the facts from both sentences we have no information or relation

about the smaller piece so we will assign the variable x to the shorter length. Having

assigned a variable to the shortest length we can use sentence 2 to denote the largest

length as x + 5. Now that we have algebraic expressions for both unknown quantities we

are ready to translate this word problem into an equation, from the first sentence we know

that the original length of this piece of wood was 50 inches this means that if we were

to add the smaller and larger piece it should equal 50 inches. So we go ahead and add the shortest

piece x with the longest piece x + 5 and set it equal to 50 as follows, so our final answer is x + (x+5)=50 and this is our equation. Alright let’s try the final example. Brenda drove three times as far as John.

Brenda drove 24 miles more than John. Once again feel free to make a drawing to

help you visualize and analyze the problem. The first step is to identify our unknowns.

After reading both sentences we see that we don’t know how many miles Brenda or John

drove so these quantities are going to be our unknowns. Next we need to assign variables

to these unknowns, once again let’s determine which of the two unknowns we have little to

no information on. Notice that we have sentences that relate Brenda’s distance to John’s

distance, but not the other way around. We have no idea what john’s distance is or

how it is related to Brenda’s distance so we will assign this quantity as our variable

and we will use the letter J. Now an expression for Brenda’s distance is going to depend

on the sentence that we use. The first sentence says that Brenda’s distance is three times

as far as John this translates to 3J or 3 times J. On the other hand if we use the second sentence we

have that Brenda’s distance is 24 more than John’s distance this translates to 24 + J.

Notice that in this example we have two variable expressions that represent Brenda’s distance.

Now the last step is to translate these expressions into an equation. Because both sentences

relate Brenda’s distance with that of John’s, it only makes sense that these two expressions

are equivalent to each other so we set both expressions equal to each other as follows.

3J=24 + J and this is our final equation. In this example we had two sentences that

related a single unknown quantity with the other unknown quantity in two distinct ways

since both sentences relate the same unknowns it is natural that both expressions are equivalent

to each other so you go ahead and set them equal to one another. Alright in our next

video we will continue going over more challenging word problems.

great!!!!!!!!