Translation Problems in 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 in a typical math Of course, this is due to a variety of reasons, many students do not bother reading word problems and if they do happen to read it they have a hard time understand them.
The best strategy to tackle word problems head on is through a plan and hold on to it. In general, word problems describe a situation where certain numbers are related to each other. For the most part some of these numbers are in trouble and are considered to be known numbers or quantities. then you must have other numbers you have no idea what their values these numbers are referred to to as your strangers. You need to determine their value using the facts of the problem. In this video we will practice translation simple word problems that contain two facts including two unknowns. The following steps will serve as a blueprint to begin with in learning how to translate word problems into equations. In a much later video we will learn how to find the solution to this word problems by actually solving the equation. For now, we must first learn how to translate the word problem into an equation.
The following three steps will serve as a guideline for you to practice translation problems in comparisons. Step 1: Read the problem carefully. (When you see a word problem just start reading it so you can get an idea of what the problem is go over. Decide what the unknowns are. (Try to from what quantities you need to settle for or trying to figure out what quantities for you have little or no information about. this is usually a tell tell sign that the amount is an unknown). Decide what the facts are. (These facts are key in determining how you will relate the quantities to each other).
Step 2: Select a variable at the Represent Unknown. Select a variable for one unknown. (Remember that you can choose any letter of the alphabet to represent this unknown. choose letters that the problem is as relevant first letter of a person's name or object for example you can use the variable N represents the name Newton or represents the variable L at the length of a rectangle, or you can just use the letter X to represent your unknown. Write an expression for the other unknown use of the variable and one of the facts. (In these problems you will have two unknowns as a result you need to find out how the two variables are related to each other and indicate them mathematically using mathematical operations such as addition, subtraction, multiplication, and division). Step 3: Read the problem again and write an equation. (I can not over emphasize the importance of read the problem over and over again making 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 of the problem to write a comparison. Okay, 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. Okay, step 1 is to read through the problem carefully and determine the unknowns and the facts. The facts of this problem are represented by the numbered sentences. Note that in this problem the unknown is the amount of money that Mary and Helena each have, as we do not explicitly tell how much money they have in their possession. Rather we given a ratio of this amount between the two persons. This relationship will be used in step 2. In step two we continue and to know 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. The question we need to ask ourselves is how do we do algebraic indicate this with a variable. From the first sentence we know that Mary has twice as much money as Helena.
We are actually given some kind of relationship between Mary's amount and Helena's amount, this is not the case for the amount of money that Helena has. as a rule you should always assign the first variable to the quantity for which you has the least amount of information. in this case we really do not know much about Helena's amount so let's go ahead and show it quantity with the letter h, now if we use this variable together with the first sentence can represent our quantity Maria's as 2h for twice as much. All we have to do now is write a comparison regarding these two expressions. Note that in sentence 2 we are told that together Maria and Helena have $ 36. This means that if we add the amount of money that Mary and Helena have they would add up to $ 36. So our equation becomes h + 2h = 36 and this is our final answer.
We successfully translated the word problem into an equation. In a later video will teach us how to solve this equation, for now we want to practice using these 3 steps that provide the framework as needed you can tackle these and future word problems. Okay, let's try the following example. A piece of wood 50 inches long is sawn 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 use skills to solve word problems. Well let's start with step 1: we must first identify our strangers, we must find out what quantities we have limited or no information for. In this case, we really do not know how much to measure each of the individual pieces so we are unknown the lengths of these two pieces of wood. Step 2: Next we need to know variables to our strangers, before we do that we need to first show a variable to the strangers that contains the least amount of information. From sentence 2 we are told that one piece 5 inches longer than the other piece.
This means that we have a piece that is larger as the other piece. We have a small and a large piece. If we look at the facts of both sentences we have no information or relationship about the smaller piece so we will assign the variable x to the shorter length. with assigned a variable to the shortest length can use our sentence 2 to indicate the largest length as x + 5. Now that we have algebraic expressions for both strangers we are ready to translate this word problem into a comparison of the first sentence we know the original length of this piece wood was 50 inches it means that if we have to add the smaller and larger piece it equal to 50 inches.
So we go ahead and add the shortest piece x with the longest piece x + 5 and set it equals 50 as follows, so our final answer is x + (x + 5) = 50 and that is our equation. Well let's let us Try the final example. Brenda rode three times as far as John. Brenda rode 24 miles more than John. Again feel free to make a drawing to help you visualize and analyze the problem. The first step is to identify our strangers. After reading both sentences we see that we do not know how many miles Brenda or John drove so these quantities are going to be our unknowns. Next we need to assign variables to let these unknowns determine again which of the two unknowns we have little to no information about. Note that we have a sentences that Brenda's distance is related to John's distance, but not the other way around.
We have no idea what John's distance is or how it relates to Brenda's distance so We will allocate this quantity as our variable and we will use the letter J. Now use an expression for Brenda's distance is going to depend on the sentence we use. The first sentence says that Brenda's distance is three times as far as John, it comes down to 3J or 3 times J. On the on the other hand, if we use the second sentence we have that Brenda's distance is 24 more than John's distance This comes down to 24 + J. Note that in this example we have two variables expressions that represent Brenda's distance. Now the last step is to translate these expressions in an equation. Because both sentences relate Brenda's distance to that of John's, it just makes sense that these two expressions are equal to each other so we both state expressions equal to each other as follows.
3J = 24 + J and this is our final equation. In this example we have two sentences that are related one unknown factor to the other unknown factor in two different ways since both sentences relate to the same unknown It is natural that both expressions are equivalent to each other so you go ahead and introduce them equal to each other. Well in our next video we will continue on about more challenging word problems..