You receive a medication order of 40 mg/kg
of body weight.
The available medication is 100 mg/ml.
How many milliliters should you give to an 8 lb 4 oz infant?
To solve this problem we'll be using proportions
which we see here below, if the units of a and c
are the same and units of b and d are the same
then a times d must equal b times c.
To set up the first proportion we'll use
the rate 40 milligrams per kilogram of body weight.
So we'll have 40 milligrams,
per one kilogram must equal the number of milligrams
for the infant which we'll call x milligrams.
Per the weight, which is given as eight pounds four ounces.
Notice in this case we can not cross multiply and solve
for x because we do not have the same units on the bottom.
Here we have kilograms, and here we have pounds and ounces.
So we'll first have to get a common unit here,
we'll convert ounces to pounds and then we'll convert
the pounds to kilograms to finally solve for x.
So we first want to convert four ounces to pounds.
You may recognize this as 0.25 pounds, but if we don't,
we can use the conversion 16 ounces equals one pound,
set up another proportion to convert four ounces to pounds.
We can say that 16 ounces is to one pound
as 4 ounces is to an unknown number of pounds,
we'll call it y pounds.
Notice in this case, the units on top
and on the bottom are the same, so we can cross multiply
and solve for y.
When cross multiplying we'll leave off the units
so 16 times y must equal one times four or 16 y equals four.
We divide both sides by 16,
we have y equals 4/16ths which does simplify to 1/4th
which would be 0.25.
Remember to convert a fraction to a decimal,
we divide.
Notice one divided four equals 0.25
and so does four divided by 16.
Which means we can now write this as 8.25 pounds
instead of eight pounds four ounces.
But notice how we still have different units on the bottom
so now we'll convert pounds to kilogram.
So for the next proportion we'll use the conversion
2.2 pounds is approximately one kilogram.
This will give us the first rate or ratio in our proportion
we can say that 2.2 pounds is to one kilogram
as 8.25 pounds,
is to an unknown number of kilograms,
we'll call it z kilograms.
Again notice how we have the same units on top
same units on the bottom,
so we can cross multiply and solve for z.
2.2 times z must equal one times 8.25.
So 2.2 z equals 8.25 divide both sides by 2.2,
z is equal to this quotient here.
8.25 divided by 2.2
is 3.75.
Which means 8.25 pounds, is equal to 3.75 kilograms.
So we finally can solve for x to determine the number
of milligrams the infant needs
and then from there we can determine the number
of milliliters the infant needs.
So we can say 40 milligrams
is to one kilogram as x milligrams is to 3.75 kilograms.
So we notice finally we do have the same units
on the top and on the bottom so now we can cross multiply
and solve for x.
We would have one times x equals 40 times 3.75.
One times x would be x.
And then we have 40 times 3.75
which would give us the number of milligrams
the infant needs.
So the infant needs 150 milligrams.
And now we can use this information to determine the number
of milliliters the infant needs, the medication comes in
100 milligrams per milliliter.
So this will be one of the rates for our last proportion.
We'll have 100 milligrams,
to one milliliter,
must equal the rate of 150 milligrams
to an unknown number of milliliters.
So if 150 milligrams to, let's call it q number
of milliliters.
Notice in this last proportion we do have the same units
on top and the same units on the bottom
so we can cross multiply and solve for q
to answer the final question.
Q times 100, must equal one times 150.
Well 100 q equals 150,
divide both sides by 100,
we would have q equals, this would be 1.5
which means you give the infant
1.5 milliliters of medication.
I hope you found this helpful.