Solving Word Problems

For: Susy L, Caro I, Mau, Lili, and Fio

To properly understand a word problem you might want to take a look at the following steps:

1. Read it (obviously)
2. Rephrase it in your own words so that you make sure you understand it.
3. Identify its parts. You will always be asked to find something using other information they do give you. So you must identify what you’re being asked for and what you are given.
4. Identify the relationship between what you’re being asked for and what you’re given. Many times, the same problem will give you the relationship. In other cases, you have to set it yourself.
5. Assign variables to information you don’t have.
6. Translate the relationship between your unknown information and known information into a math expression. There are times in which the relationship will already be expressed as a math expression so that you only have to put in proper variables.
7. Carry out the proper operations.
8. Check your work

For steps 3-5, it sometimes helps to draw a picture.

The first example is very easy, just to illustrate the process. The second one gets a bit harder. If you have any particular word problem you would like help with, please let me know.

PROBLEM 1:

Step 1: Read it

Pedro has 5 more apples than Laura. Laura and Pedro have 27 apples in total. How many apples does Laura have?

Step 2: Understand it

Step 3: Identify its Parts

What are you being asked for: The amount of apples Laura has
What you know: Laura and Pedro have 27 apples. Pedro has 5 more apples than Laura.
What you don’t know: Number of apples Pedro has. Number of apples Laura has

Step 4: Identify a Relationship

In this case, the relationship is given to you in the problem. It is what you know: that Laura and Pedro have 27 apples, and that Pedro has 5 more apples than Laura.

Step 5: Assign Variables

P=Number of apples Pedro has
L=Number of apples Laura has
Variables help you replace words with letters

Step 6: Translation

Relate what you know to your variables (what you don't know)

You now have two equations that relate what you know to what you don’t know:
L+P=27
P=5+L

Step 7: Solve

You just have to solve for L by substituting P in the first equation

L+P=27
L+(5+L)=27
2L+5=27
2L=27-5
2L=22
L=22/2
L=11 (This is your answer)

Step 8: Check your work

L+P=27 and P=5+L must be equal to each other for the value of L=11. Replace L for 11 in both equations. You should get the same value for P.

L+P=27
11+P=27
P=27-11
P=16

P=5+11
P=16

PROBLEM 2 (This one I got off the internet):

Step 1: Read it

A piece of Wire 46 inches long is bent into the shape of a rectangle having length x and width y. Express the area A of the rectangle as a function of x.

Step 2: Understand it

You have a 46 inch wire that you must bend in order to make a rectangle. The rectangle will have sides of length x and width y. Come up with a function for the area of the rectangle using only the variable x. (Making a picture sometimes helps)

Step 3: Identify its Parts

What are you being asked for: Area in terms of x, or A(x)
What you know: Perimeter equals 46 inches since it must equal the length of the wire. The shape is a rectangle. The length of the rectangle equals x and the width equals y
What you don’t know: A(x)

Step 4: Identify a Relationship

You’re looking for the area of a rectangle, which is length times width.

A=l*w

The perimeter of a rectangle equals the sum of its sides.

P=l+l+w+w
P=2l+2w

Step 5: Assign Variables

P=Perimeter=46
A=Area
The variables for the sides have already been assigned, x and y.
l=x and w=y

Step 6: Translation

In this case, translation consists in replacing variables

l=x w=y A=l*w
A=x*y

l=x w=y P=2l+2w P=46
46=2x+2y

Step 7: Solve

As said before, they ask for Area (A) in terms of x. Right now, you have Area in terms of x and y.

A=x*y

You need to replace y for an expression that contains only x. The only relationship you can use for this is 46=2x+2y.

Solve for y

46=2x+2y
46=2(x+y)
46/2=x+y
23=x+y
23-x=y

Replace y for 23-x on the function for Area.

A=x*y
A=x*(23-x)
A(x)=23x-x^2 (This is your answer)

More Help: If you still need help, you can always google “Translating Word Problems”, or “Solving Word Problems”. There are hundreds of ways to approach a word problem. You just have to find the one that works best for you.