## Word Problems: Direct Variation

Direct variation type word problems encompass one variable, which is directly proportional to another variable:

y = kx,

where k is referred to as the constant of proportionality.

Direct variation word problems often contain verbiage such as:

- "varies directly as"

- " varied directly as"

- "directly proporation to"

1) Recognizing the word problem consists of direct variation as exemplified by presence of verbiage listed above;

2) Writing an equation containing known values for both variables resulting in an expression containing only the unknown representing the constant of proportionality;

3) Solving the equation for the constant of proportionality;

4) Using the calculated constant of proportionality to determine the value of one of the variables given the other.

Example:

Solution:

The amount of money raised at a charity
fundraiser is directly proportional to the number of attendees.
The amount of money raised for five attendees was $100. How
much money will be raised for 60 attendees?

Solution: