Question

The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog 3/5 milligram of the medicine, which equation relates the weight, w, and the dosage, d?
A. d=1/50w
B. d=3/5w
C. d=18w
D. d=50w

Answer 1

Answer:

Option A is correct

$d = \frac{1}{50}w$

Step-by-step explanation:

Direct variation says that:

$y \propto x$ then;

the equation is in the form of

$y=kx$, 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;

$d =kw$         .....[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;

$\frac{3}{5} = 30k$

Multiply both sides by 5 we have;

$3 = 150k$

Divide both sides by 150 we have;

$\frac{3}{150}=k$

Simplify:

$k = \frac{1}{50}$

⇒$d = \frac{1}{50}w$

therefore, equation relates the weight, w, and the dosage, d is:

$d = \frac{1}{50}w$

Answer 2

Answer:

simple answer a

Step-by-step explanation: