Welcome to an example of
a Pediatric Medication Calculation,
they'll be determined using proportions.
Proportion is made when we set two ratios
or rates equal to each other as we see here,
where as long as the units of a and c
are the same and the units of b and d are the same,
then a times d must equal b times c.
These are called cross products.
So if we have one unknown,
we can solve for the unknown using the cross products.
Here we're given a 20 pound, six ounce child
is to receive medication ordered at 20 micrograms
per kilogram of body weight.
How many micrograms should the child receive?
To set up the proportion we'll begin with
a known rate of 20 micrograms per kilogram, so we can write
this as 20 micrograms per one kilogram
must equal to the second rate would deal
with the given weight of the child.
Since kilograms is weight, the 20 pounds, six ounces
must go on the bottom.
the numerator would be the number of micrograms
which is unknown, so we'll say x micrograms.
Notice in this form we cannot cross multiply
because our denominator contains different units.
Here we have kilograms and here we have both pounds
and ounces.
So first convert these two to a common unit
will convert the six ounces to pounds,
and then we'll have to convert the pounds
to kilograms.
So again for the first step we're going to convert
six ounces to pounds, and we'll use the conversion
16 ounces equals one pound.
So these two will give us our first ratio
for the proportion.
We'll have 16 ounces is to one pound
as six ounces would be to an unknown number
of pounds, which we'll call y pounds.
Notice we do have the same units
on the top, and on the bottom,
so we can go ahead and cross multiply and solve for y.
When cross multiplying, we will leave off the units.
So we'll have 16 times y equals one times six.
16 times y is 16y.
Equals one times six of course is six.
Divide both sides by 16.
So we have y equals 6/16 or 3/8, that simplifies.
And we do want to convert this to a decimal,
and then we'll round to two decimal places.
So we convert this to a decimal,
we'll divide three by eight.
Three divided by eight is 0.375.
Do a round to the hundredth or two decimal places,
notice how this five here's our decision maker.
Five or more, we round up,
four or less we round down.
Because we have a five here.
Round up by changing this to 0.38.
Which means six ounces is approximately 0.38 pounds,
so now we can rewrite this as 20.38 pounds.
Notice how we still have different units on the bottom.
Here we have kilograms, and here we have pounds.
So now we'll convert 20.38 pounds to kilograms
using another proportion.
The conversion we'll use is 2.2 pounds
is approximately one kilogram.
So this will give us our first ratio,
2.2 pounds is to one kilogram
as 20.38 pounds is to an unknown number of kilograms,
we'll call it z kilograms.
We have the same units on top,
and on the bottom, so we can cross multiply
and solve for the unknown,
so we have 2.2 times z must equal one times 20.38.
So we have 2.2z equals 20.38,
divide both sides by 2.2.
So z will be equal to this quotient here,
which we'll have to round.
So 20.38 divided by 2.2 is going to be approximately
9.26 if you round this to two decimal places.
Again here we have a three to the right,
keeping this a six, so 9.26.
So finally we have the proportion that we need
to solve this problem.
We can replace 20.38 pounds with 9.26 kilograms.
So 20 micrograms is to one kilogram
as x micrograms is to 9.26 kilograms.
So because we have the same units on top
and on the bottom, we can now cross multiply
and solve for x.
One times x must equal 20 times 9.26.
Well one times x is just x,
and 20 times 9.26 will give us
the number of micrograms needed for this child.
185.2 micrograms.
I hope you found this helpful.