Question

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.

Answer 1

m = 0.01w
So for a 10 pound dog, m = 0.01(10) = 0.1 mg
Also, since 10 pounds is 1/5 of 50 pounds, then 1/5 of 0.5 mg is 0.1 mg.
With either calculation, the dose is 0.1 mg

Answer 2

0.1 milligrams

Explanation:

We have been given that the number of milligrams, m, varies directly with the weight of the dog, w.

We know that two directly proportional quantities are in form
`y=kx`, where y is directly proportional with x and k is constant of proportionality.

Upon substituting our given variables in inversely proportion, we will get:

`m=kw`

We have been given that veterinarian knows that a 50-pound dog gets 0.5 milligram of a certain medicine.

Let us find constant of proportionality using our given information.

`0.5=k(50)`

`(0.5)/(50)=(50k)/(50)`

`k=0.01`

So our required equation would be
`m=0.01w`.

Now, we will substitute
`w=10` in our equation to solve for medicine needed for a 10-pound dog.

`m=0.01(10)`

`m=0.1`

Therefore, the vet will give 0.1 milligrams of medicine to give a 10-pound dog.