#### Examples - Variation Word Problems

# Algebra Word Problem Solver solves many types of Inverse Variation problems.

## See Other Variation Word Problem Examples solved by the Algebra Word Problem Solver.

- Solving Inverse Variation Word Problems
- Solving Directly Proportional Variation Word Problems
- Solving Direct Variation - Varies as the Square Word Problems

###### What You Enter

### y varies inversely proportional to x. y=3 when x=25. Find y when x= 7.

###### What You Get

Y = k/X Inverse Variation Statement 3 = k / 25 // Y = 3 WHEN X = 25 . Substitute values. k = 75 // Constant of Proportionality Y = 75 / X // Y as a Function of Y = (75 / 7 ) // X = 7 . Substitute value. Y = (75 / 7 ) // Y WHEN X = 7

Solution: Y = (75 / 7 )

####
Solving Variation Word Problems

Common Variation problems found in Algebra Word Problems in algebra courses are of the following types. The Algebra Word Problem Solver can be used to solve these.

Note that in all examples below, k is the constant of proportionality.

Direct Variation:
- Common phrases to identify this type include Varies Directly, Directly Proportional,
- Here are some examples using these:
- y varies directly as x… Translates to y=kx
- y is directly proportional to x… Translates to y=kx

- A variation to the linear examples above are shown below where y varies with the square of x or y varies with the cube x: (Note that the variables do not need to be x and y).
- y varies directly as the square of x… Translates to y=kx
^{2}
- y is directly proportional to x cubed… Translates to y=kx
^{3}

Inverse Variation:
- Common phrases to identify this type include Varies Inversely, Inversely Proportional
- Here are some examples using these:
- y varies inversely as x… Translates to y=k/x
- y is inversely proportional to x… Translates to y=k/x

- A variation to the linear examples above are shown below where y variesinversely with the square of x or y varies inversely with the cube x.
- y varies inversely as the square of x… Translates to y=k/x
^{2}
- y is inversely proportional to the cube of x… Translates to y=k/x

Here are some examples using these:
- If y varies directly as x… Translates to y=kx
- If y is directly proportional to x… Translates to y=kx

Typical Problems:
- Typical problems generally contain another part that gives a value for x when y has a given value.
- This allows you to calculate the constant of proportionality.
- Given the proportionality constant, one now has the equation of the variation problem.
- Examples
- If y is inversely proportional to x squared, and y=-8 when x=-4, what is y when x = -8?
- If d varies directly as the square of t, and d = 11 when t = 3, find d when t = 6.
- If y varies directly as x
^{2}, and y = 8 when x = 2, find y when x = 3.

- These and many others can be solves using the Algebra Word Problem Solver.
- To see actual solved problems, see the problem below, and click on the See Also links.

- y varies directly as x… Translates to y=kx
- y is directly proportional to x… Translates to y=kx

- y varies directly as the square of x… Translates to y=kx
^{2} - y is directly proportional to x cubed… Translates to y=kx
^{3}

- y varies inversely as x… Translates to y=k/x
- y is inversely proportional to x… Translates to y=k/x

- y varies inversely as the square of x… Translates to y=k/x
^{2} - y is inversely proportional to the cube of x… Translates to y=k/x

- If y is inversely proportional to x squared, and y=-8 when x=-4, what is y when x = -8?
- If d varies directly as the square of t, and d = 11 when t = 3, find d when t = 6.
- If y varies directly as x
^{2}, and y = 8 when x = 2, find y when x = 3.