Answer:
Option A is correct
[tex]d = \frac{1}{50}w[/tex]
Step-by-step explanation:
Direct variation says that:
[tex]y \propto x[/tex] then;
the equation is in the form of
[tex]y=kx[/tex], where k is the constant of variation
As per the statement:
The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog.
Here, w represents the weight and d represents the dosage
then ,by definition of direct variation we have;
[tex]d =kw[/tex] .....[1]
It is also given that if the veterinarian gives a 30-pound dog 3/5 milligram of the medicine
⇒w = 30 pound and d = 3/5 milligram
Substitute in [1] we have;
[tex]\frac{3}{5} = 30k[/tex]
Multiply both sides by 5 we have;
[tex]3 = 150k[/tex]
Divide both sides by 150 we have;
[tex]\frac{3}{150}=k[/tex]
Simplify:
[tex]k = \frac{1}{50}[/tex]
⇒[tex]d = \frac{1}{50}w[/tex]
therefore, equation relates the weight, w, and the dosage, d is:
[tex]d = \frac{1}{50}w[/tex]
