Writing Equations to solve

Word Problems

One way to solve word problems is to look for key words to help you write

an equation.

You must decide what the variable represents – it should be what you are

trying to find!

Here are two sample word problems and solutions:

You have a suitcase that can hold up to 23 kilograms. You are

packing clothes and want to make sure you have space left over for a PlayStation you plan to buy before

your trip. If the PlayStation weighs 3.75 kg, how many clothes

can you pack?

Clothes + Playstation = Total weight

x + 3.75 = 23

- 3.75 - 3.75

x = 19.25 kg

Let x = amount of clothes

John is 3 years less than twice his sister’s age. If John is 11, how old is his

sister?

John’s age

twice his sister’s age

3 years less than

11 = 2s - 3

Let s = sister’s age

Note: A common key word that indicates where to put the equal sign is the word ‘IS’

Another way to solve word problems is to organize the information.

For example, you may find it useful to create a table.

Here is a sample word problem and solution:

Here is a table with information from the first sentence filled in algebraically.

Now information from the second sentence is included algebraically.

An equation is written from the information in the table.

Finally, solve the equation to find the answer:

h + 8 + 5 = 2 ( h + 5)

h + 13 = 2h + 10 -h -h

13 = h + 10 -10 -10

3 = h

Therefore, Chuck is 3 and Cara is 11!

Try this strategy!

Cross out with pencil (or highlight) the information as you use the information in your chart or diagram.

Highlight (in a different color) what is left and use this to write your equation.

Solve the equation and answer the problem.

Write equations for the following problems on

a white board.Check your answers on the following slide.

Seven more than three times a number is 31

7 + 3n = 31

The quotient of a number and 9 increased by 3

is -7

The width of a singles tennis court is 27

feet. This is one foot more than one-third

of the length.

Joanne starts with $5 in her savings account and adds $10 every week. Write an expression with a variable

that tells how much she will have in her account after n

weeks.

How much will Joanne have in her savings account after 9

weeks?