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

simple answer a

Explanation:

Answer 2

Option A is correct

`d = (1)/(50)w`

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;

`(3)/(5) = 30k`

Multiply both sides by 5 we have;

`3 = 150k`

Divide both sides by 150 we have;

`(3)/(150)=k`

Simplify:

`k = (1)/(50)`

⇒
`d = (1)/(50)w`

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

`d = (1)/(50)w`