# Word Problems

A word problem requires you to find an answer from the facts of the problem.

Here are some steps to follow:

• Do you understand all the words used in stating the problem?
• What are you asked to find?
• Can you restate the problem in your own words?
2. Devise a plan. Pick an approach and give it a try. For example:
• Guess and check.
• Look for a pattern.
• Draw a picture.
• Use a chart.
• Set up variables and solve an equation.
3. Carry out the plan.
4. Check your answer against the words of the problem to be sure that it makes sense.

Below are a few words and phrases to look out for when translating from English to mathematical symbols.

 ENGLISH MATH SYMBOLS $3$ more than a number $3$ greater than a number $3$ units longer than/ older than/ taller than/ heavier than a quantity $3+x$ 5 less than a number 5 units shorter than/ younger than/ lighter than/ nearer than a quantity $x-5$ $7$ diminished by a number / decreased by a number $7-x$ twice a number $2\cdot x$ $6$ times as many as a number $6$ times as long as/ as old as/ as tall as/ as heavy as a quantity $6\cdot x$ half as much as a number $\frac{1}{2}x$ two thirds as much as a number $\frac{2}{3}x$ the quotient of a number and $8$ a number divided by $8$ $\frac{n}{8}$ the square of a number ${x}^{2}$ the cube of a number ${x}^{3}$ is/is equal to/is the same as = is less than < is greater than/is more than > is at most / is no more than $\le$ is at least / is no less than $\ge$

Also, the following four definitions are important:

Example 1:

Five times a number $x$ is less than the sum of 3 and a number y .

"5 times a number $x$ " indicates multiplication: 5 x .

"is less than" indicates the < relation.

"the sum of $3$ and a number y " indicates addition: $3+y$

Putting it all together:

$5x<3+y$

Example 2:

Ten more than the quotient of a number $x$ and $30$ is equal to $15$ .

"Ten more than" indicates addition: $10+$ .

"the quotient of a number $x$ and 30" indicates division: $\frac{x}{30}$

"is equal to 15" indicates the = relation: = $15$

Putting it all together:

$10+\frac{x}{30}=15$