Word problems do not come with equations. To solve a word problem, it is often helpful to rewrite the problem using mathematical notation.
Here are some strategies for approaching a word problem:
(Please note that these examples do not represent a complete list of key words.)
Now you have the basic tools to begin constructing equations from word problems. Take care to make your work clear and organized throughout your solution.
I want to make an apple-orange fruit salad for a picnic. My recipe calls for 2 apples for every 3 oranges. If I want to use 6 apples, what is the total number of fruit I need for the salad?
"2 apples for every 3 oranges" tells us that for every apple there needs to be oranges. I'm using apples, so I will need oranges. The problem asks for the total number of fruit, which would be the number of apples plus the number of oranges: .
Today Beatrice is 3 times as old as Kelly. In 3 years she will be 4 times as old as Kelly was 1 year ago. How many years from today will Beatrice be twice as old as Kelly?
Let be the number of years it takes from today for Beatrice to be twice as old as Kelly. Before we can find , however, we need to determine how old Kelly and Beatrice are right now. Let and be Beatrice's and Kelly's ages respectively. Now let's set up a couple equations.
"Today Beatrice is 3 times as old as Kelly" translates into:
"In 3 years she will be 4 times as old as Kelly was 1 year ago" translates into this equation:
Combining the two equations we get:
for which , which then means .
Now that we know Beatrice's and Kelly's ages, we can find to answer the problem's question "How many years from today will Beatrice be twice as old as Kelly?" This can also be rewritten into an equation, which we can then solve for :