You receive an order
for 10 milliunits per kilogram per minute.
The solution is labeled 40 units per 100 milliliters.
The patient weights 198 pounds.
What is the correct rate or flow rate
in milliliters per hour?
So to find the flow rate,
we'll have to perform several conversions.
Notice how the order is given in milliunits per kilogram
but the weight is given in pounds.
Let's begin by converting 198 pounds to kilograms,
and we'll do this using a proportion.
Looking at our conversions below,
notice that one kilogram is equal to 2.2 pounds,
so we can say one kilogram is to 2.2 pounds
as an unknown number of kilograms,
which I'll call X kilograms, to the weight at 198 pounds.
And before we cross multiply and solve for X,
it's important to recognize that we have
the same units on the top and the same units on the bottom.
If we did not have this,
we'd have to perform a conversion first.
But because we do, 2.2 times X is 2.2 X
must equal one times 198.
Dividing both sides by 2.2,
this comes out very nicely on the right.
This is equal to 90,
so 90 kilograms is equal to 198 pounds.
Now that we know the patient's weight in kilograms,
let's determine how many milliunits
the patient needs per minute.
The order calls for 10 milliunits per kilogram,
so 10 milliunits per one kilogram
must equal an unknown number of milliunits,
we'll call it Y milliunits,
to the patient's weight of 90 kilograms.
Once again, we have the same units on top,
same units on the bottom,
so we can cross multiply and solve for Y.
So one times Y is Y.
10 times 90 is 900.
Which means the patient needs 900 milliunits per minute.
So again, we can write the order for this particular patient
as 900 milliunits per minute,
but notice how we want the flow rate in milliliters per hour
so now let's convert this rate into milliunits per hour,
and then we'll determine how many milliliters we need.
So for the next proportion, 900 milliunits per one minute
must be equal to some number of milliunits,
we'll call it Z milliunits, per one hour,
but because we need the same units on the bottom,
notice here we have minutes, instead of writing one hour,
one hour is equal to 60 minutes,
so I'll write this as 60 minutes.
Again, we have the same units on the bottom,
same units on the top,
so now we can cross multiply and solve for Z.
One times Z is Z.
900 times 60 is equal to 54,000,
which means now we can write the order
as 54,000 milliunits per one hour.
For the next step, we'll convert the 54,000 milliunits
to units, then once we find the number of units,
we can determine the number of milliliters per hour.
Let's go and continue this one the next slide.
Again, now we're going to convert milliunits to units.
Going back to the previous slide just for a moment,
notice how 1,000 milliunits is equal to one unit.
So this will give us the left side of the proportion.
1,000 milliunits is to one unit as 54,000 milliunits
is to an unknown number of units, we'll say A units.
Once again, we have the same units on top,
same units on the bottom.
Cross multiply and solve for A.
1,000 times A, or 1,000 A must equal one times 54,000.
Divide both sides by 1,000.
So we have A equals 54.
So if A's equal to 54, that means 54,000 milliunits
is equal to 54 units, and therefore,
we can now write the order as 54 units per hour.
Now we need one more proportion.
We need to determine how many milliliters
is required for 54 units.
So going back to the given information just for a moment,
notice how the solution has a rate
of 40 units per 100 milliliters.
So they can say 40 units is to 100 milliliters
as 54 units is equal to an unknown number of milliliters,
which we'll say B milliliters.
And finally, once again, we have the same units on the top,
same units on the bottom,
so now we can cross multiply and solve for B.
So we have 40 times B, that's 40 B,
equals 100 times 54, that's 5,400.
Divide both sides by 40.
5,400 divided by 40 is equal to 135.
Which means that the patient requires 54 units,
that would be equivalent to 135 milliliters of the solution
and therefore, the flow rate for this patient
is 135 milliliters per hour.
I hope you found this explanation helpful.