SAT Math Tutorial
Direct Variation vs. Inverse Variation
Intro
The SAT often asks questions about direct variation and inverse variation. These questions use wording like “…varies directly with…”, “…varies inversely with…”, “…is directly proportional to…” and “…is inversely proportional to…”
The formulas for direct and inverse variation are as follows.
Direct Variation
As one variable increases, the other variable increases proportionately.
Inverse Variation
As one variable increases, the other variable decreases proportionately.
Here is a typical SAT variation problem.
Sample Problem
Solution
The first step for this problem is to determine whether to use the direct variation formula or the inverse variation formula.
In this case, the problem states that “ varies directly with
.” Thus, the relationship between
and
is a direct one, requiring the direct variation formula,
.
Next, find the value for by substituting the appropriate values for
and
into the direct variation formula.
Once the value of is determined, substitute it into
to see the true relationship between
and
.
Finally, the question asks for “the value of when
.” So substitute 48 for
in the equation above and solve for
.
Thus, the answer is .
Challenge Questions
How would the answer change if the question stated that “ varies inversely with
?” What if it stated that “
varies inversely as the square of
?”
About The Author
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Jared, founder of The Knowledge Roundtable, is passionate about the advancement of knowledge. He has a B.S. in astronomy and physics from UMass and an MBA in Advanced Financial Analytics, also from UMass. He has a day job as a Data Scientist in Boston. He has over 500 hours of tutoring experience... |
