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Since the "distance, d, a string is stretched varies directly with the force, F", this means that we have the equation
Start with the given equation
Divide both sides by 12 to isolate k
So the variation constant is
(or in decimal form
Go back to the original equation
Since we want the distance when the "force of 30 pounds is applied", we need to plug in
Convert to decimal form
So the distance is 7.5 inches when a force of 30 pounds is applied.