Word problems can be tricky. Often it takes a bit of practice to convert the English sentence into a mathematical sentence. This is what we will focus on here with some basic number problems, geometry problems, and parts problems.
A few important phrases are described below that can give us clues for how to set up a problem.
• A number (or unknown, a value, etc) often becomes our variable
• Is (or other forms of is: was, will be, are, etc) often represents equals (=)
x is 5 becomes `x=5`
• More than often represents addition and is usually built backwards,
writing the second part plus the first Three more than a number becomes `x + 3`
• Less than often represents subtraction and is usually built backwards as well, writing the second part minus the first
Four less than a number becomes `x − 4`
Using these key phrases we can take a number problem and set up and equation
and solve.
Example
If 28 less than five times a certain number is 232. What is the number?
Set the number to `x`
| `5x − 28` | multiply the unknown by 5, than subtract 28 |
| `5x − 28 color(red)(= 232)` | Is translates to equals |
| `5x − 28 = 232` | Solve Linear Equation |
| `5x − 28 color(red)(+28)= 232color(red)(+28)` | |
| `5x=260` | |
| `(5x)/color(red)(5)=260/color(red)(5)` | |
| `x= 52` | |
Example
Fifteen more than three times a number is the same as ten less than six times the number. What is the number
| `3x+15` | Fifteen more than three times a number |
| `6x−10` | Ten less than six times the number |
| `3x+15=6x−10` | Is between the parts tells us they must be equal |
| `3x+15color(red)(-3x)=6x−10color(red)(-3x)` | |
| `15color(red)(+10)=3x−10color(red)(+10)` | |
| `25=3x` | |
| `25/color(red)(3)=(3x)/color(red)(3)` | |
| `25/3=x` | |
