Word Problems


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:

  1. Always start off by reading the entire problem.
  2. List information you know and assign variables to anything you don't know.
  3. Identify what the problem is asking for.
  4. Look for key words to identify which operations you will need to use. Here are some examples:

Addition: more than, increased by, total of, sumSubtraction: less than, subtract, difference Multiplication: times, product of, multiplied byDivision: per, quotient of, percent, ratio of \begin{array}{ll} \textbf{Addition: } & \text{more than, increased by, total of, sum} \\ \textbf{Subtraction: } & \text{less than, subtract, difference } \\ \textbf{Multiplication: } & \text{times, product of, multiplied by} \\ \textbf{Division: } & \text{per, quotient of, percent, ratio of} \\ \end{array}

(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.

Application and Extensions

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 32\frac{3}{2} oranges. I'm using 66 apples, so I will need 6×32=96 \times \frac{3}{2} = 9 oranges. The problem asks for the total number of fruit, which would be the number of apples plus the number of oranges: 6+9=156+9=15. _\square


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 xx be the number of years it takes from today for Beatrice to be twice as old as Kelly. Before we can find xx, however, we need to determine how old Kelly and Beatrice are right now. Let BB and KK 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:
B=3KB = 3K
"In 3 years she will be 4 times as old as Kelly was 1 year ago" translates into this equation:
B+3=4(K1)B + 3 = 4(K-1)
Combining the two equations we get: (3K)+3=4(K1)(3K) + 3 = 4(K-1)
for which K=7K=7, which then means B=21B=21.

Now that we know Beatrice's and Kelly's ages, we can find xx 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 xx: B+x=2(K+x)21+x=2(7+x)21+x=14+2xx=7 \begin{aligned} B + x &= 2 (K+x)\\ 21+ x &= 2 (7+x)\\ 21 + x &= 14 + 2x\\ x &= 7 \quad_\square\ \end{aligned}

Note by Arron Kau
7 years, 4 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


There are no comments in this discussion.


Problem Loading...

Note Loading...

Set Loading...