ACT Preparation / Unit 11 ACT 1031 worked example, 60 to 90 seconds
Solving a Variation Problem
The idea
A variation problem is solved in four steps. First, translate the sentence into an equation with a constant k: directly means multiply, inversely means divide, and a square or a root applies to its own variable. Second, substitute the given values to find k. Third, write the equation with k known. Fourth, substitute the new values and solve.
In practice
Worked example, an invented model: a signal's strength I varies inversely with the square of the distance d from its source, and at 2 meters it is 90 units. Step one: I = k/d². Step two: 90 = k/4, so k = 360. Step three: I = 360/d². Step four: at 6 meters, I = 360/36 = 10 units.
Where people slip
Apply the square to the variable only, not to k. Tripling the distance divides the strength by nine, not by three.
Your place on the trail
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