Translating Problems into Equations (Level

2) In this video we are going to continue translating

problems into equations, this time around we will go over more challenging examples.

Making sure we use the 3 step plan introduced in the previous video. Alright let’s go

over the first example. Translate each problem into an equation.

The length of a rectangle is one meter more than its width. The perimeter of the rectangle

is 60 m. In this example we are dealing with a rectangle

so let’s go ahead and draw a rectangle to help us visualize and analyze this problem.

Recall that the first step, is to identify the unknown variables, in this example the

unknown quantities are the length and width of the rectangle. Having identified our unknowns

we now have to assign variables to them. As As a rule of thumb we first want to assign the

variable to the quantity for which we have the least amount of information. In this problem

notice that we have a description that relates the length with the width, but we don’t

have a description that relates the width with the length. This means that we should

assign the variable to the width so let’s assign the letter x to it. Now that the width

is represented by the variable x, the length of this rectangle would be denoted as x + 1

since the length is one meter more than the width. Having assigned variables to both unknown

quantities we are ready to translate the word problem into an equation. Notice that we are

given that the perimeter of this rectangle is equal to 60 meters. We are going to use

this fact in combination with the variable expressions and relate them to form an equation. In

order to accomplish this, we need to make use of a formula specifically the formula

for the perimeter of a rectangle. The perimeter is just going to be equal to the sum of all

the sides of this rectangle in other words twice the length plus twice the width. In

this problem we know that the perimeter is equal to 60, in addition we also know that

the width is represented by the variable x, and the length is represented by the variable

expression x + 1, substituting these expressions into the formula results in the following

equation, 60=2x + 2(x+1) and this is our equation. Keep in mind that you might have

to use formulas in order to successfully translate a word problem into an equation. It all depends

on the type of word problem that you are face with. Alright let’s try the next example. A triangle has two equal sides and a third

side that is 15 cm long. The perimeter of the triangle is 50 cm. In this example we are dealing with a triangle

so let’s go ahead and draw a triangle. Lets first identify the unknowns in this problem,

notice that we are given the measurement of one side of the triangle but have no idea

what the measurement of the other two sides are. For this problem the unknowns are the measurements

of these two sides of the triangle. Next let’s assign variables to these unknowns, from the

first sentence we are told that this triangle has two equal sides so we are actually dealing

with an isosceles triangle, a triangle that has two of its sides with the same measurement

this means that we can assign the same variable to both sides since they are equivalent, so

let’s assign each side with the variable x as follows. Now it’s just a matter of translating

these expressions into an equation. We first need to figure out how to relate all of these

expressions with one another. Notice that we are told that the perimeter is equal to

50 cm. We can relate all the expressions by using the formula for the perimeter of a triangle.

We essentially need to add all the sides of the triangle, so our equation will be equal

to: x + x + 15=50, and this is our final answer. Alright up to this point we have been

going over examples that contain two unknowns, Now let’s try some examples that contain

3 facts about 3 unknown. Luis is three times as heavy as his luggage.

His luggage is 20 lbs heavier than his backpack. The weight of Luis, his luggage and back pack

total 170 lbs. In this example we actually have 3 unknowns

as oppose to 2 unknowns like in the previous problems. Regardless of the number of unknowns

the procedure is essentially the same we first need to identify our unknowns. After reading

the problem it is clear that we are dealing with three unknowns, the first unknown is

Luis’s weight, the second unknown is the weight of the luggage, and the third unknown is

the weight of the back pack. Having identified the unknowns we now need to choose a variable

and represent the rest of the unknowns with this variable. First, let’s figure out which

unknown we absolutely have no information about. We know that Luis’s weight is 3 times

the weight of his luggage, we also know that his luggage is 20 lbs heavier than his back

pack, but we have no idea how the backpack is related to the other unknowns, so let’s

go ahead and represent the weight of his back pack with the variable x, this way the weight

of the luggage can be expressed as x + 20, and Luis’s weight can be expressed as 3

times the weight of the luggage or using our expressions as 3(x + 20), now we need to translate

these expressions into an equation. In the last sentence we are told that the combined

weight of the luggage, back pack and Luis’s weight is equal to 170 lbs. So we can express

this fact as follows, x + (x+20) + 3(x+30)=170 and this is our equation. When dealing

with multiple unknowns the procedure is essentially the same, just be a bit more careful and make

sure you relate the correct unknowns with one another. Alright let’s go over the next

example. Maribel, Dave, and Henry have $180 together.

Maribel has three times more money than Dave. Dave has two times more money than Henry. Similar to the previous problem we first need

to identify all of the unknown quantities. In this particular problem the unknown quantities

are the amount of money that each person has. In this example we have three unknown quantities.

Once we have determined the unknown quantities we are ready to assign variables to them.

Let’s first determine which unknown quantity we have the least information on. We know

that Maribel has 3 times more money than Dave. We also know that Dave has two times more

money than Henry, but we have no information of how Henry’s amount is related to the

other two amounts. Hence we will assign the variable x to Henry’s amount, this means

that Dave’s amount will be represented as: 2x, and lastly Maribel’s amount will be

represented as: 6x. Having assigned a variable to each unknown quantity we are ready to translate

the word problem into an equation. We know that if we were to add the amount of all three

individuals it would add up to 180 dollars, so we can denote this relation as: 6x + 2x

+ x=180, and this is our equation. Alright let’s go over the final example.

A pipe ten feet long is cut into three pieces. One piece is one foot longer than the shortest

piece and two feet shorter than the longest piece.

Alright this word problem is perhaps the most challenging problem in this video. Let’s

use everything that we learned to tackle it. Let’s first make a drawing of our pipe broken

into 3 pieces. Let’s first start by identifying the unknowns, in this example we have no idea

how much each of the pieces measure. So the length of each of the pieces will be our unknowns.

Next let’s go ahead and assign variables to each of the unknown lengths. Because we

have three distinct pieces we will label them as the shortest, medium and longest piece

so we can easily distinguish them. From the second sentence we are told that one piece

is one foot longer then the shortest piece. So let’s go ahead and assign a variable

to the shortest piece, let’s assign the variable x, with this assignment the medium piece will

be denoted as x + 1. Finally we are also given that this same piece (the medium piece) is

two feet shorter than the longest piece. Let’s think about this, if the medium piece is two

feet shorter than the longest piece that means that the longer piece is 2 feet longer than

the medium piece, in other words it can be denoted as x + 1 the length of the medium

piece + 2 since it is 2 feet longer. Having assigned the variables to all three unknowns

we are ready to translate the word problem into an equation. From the first sentence

we know that the original pipe length was equal 10. So if we were to add the individual

pieces they should add up to 10. So our final equation is equal to: x + (x+1) + [(x+1)+2]

=10. Alright make sure you read the word problem as many times as you need to. You

really need to understand the problem before you start identifying unknowns and assigning

variables to them. Ok in our next video we will expand the skills developed so far and

start solving word problems over a given domain.

Hi there, Isn't it 3(2x) or 6x for Maribel? Please clarify. Thank you for your time.