A veterinarian knows that a 50-pound dog gets 0.5 milligram of a certain medicine, and that the number of milligrams, m, varies directly with the weight of the dog, w. The vet uses these steps to find the amount of medicine to give a 10-pound dog.

Step 1 Find the constant of variation.
k = StartFraction 0.5 Over 50 EndFraction = 0.01
Step 2 Write the direct variation equation.
m = 0.01 w
Step 3
Substitute 10 into the equation to find the dosage for a 10-pound dog.
10 = 0.01 w
Step 4
Solve for w.
10 = 0.01 w. w = 1000.

The 10-pound dog needs 1000 milligrams.

In which step did the veterinarian make the first error?