Welcome to an example
of a dosage calculation, that requires multiple steps.
The order is for 150 milligrams
and the available medication is one grain per tablet.
How many tablets should you give the patient?
We're going to solve this problem using proportions,
where we set two rates or ratios equal to each other
as we see here, and then,
as long as the units of a and c are the same,
and the units of b and d are the same,
we can cross multiply, and solve for the unknown value.
Notice here, a times d is equal to b times c.
Looking at the given information,
notice how the available information
is one grain per tablet, which will be our first rate,
so we have one grain per one tablet.
Now the second rate will contain the order
of 150 milligrams, so the rate will be 150 milligrams,
to an unknown number of tablets, so we'll say x tablets.
Now analyzing this proportion,
notice how the units on top are not the same,
which means we cannot cross multiply in this form,
we have to perform a conversion.
We have to convert grains to milligrams,
or milligrams to grains.
To do this conversion we'll set up a different proportion,
using one of the conversions given here below.
Let's go ahead and convert 150 milligrams to grains.
So we want to know, 150 milligrams,
to an unknown number of grains, would be equal to,
and now for the second rate or ratio,
we use one of these conversions here,
1/60 of a grain equals one milligram,
if we multiply both sides of this equation by 60,
we can say one grain is equal to 60 milligrams.
Let's go and use this conversion here,
so the second rate or ratio is going to be
60 milligrams to one grain.
Now notice how we have the same units on top,
same units on the bottom,
so now we can cross multiply and solve for x.
When we do this we are going to leave off the units
to write the equation, so we'll have x times 60, that's 60x,
equals 150 times one, which is 150.
Again, 60x equals 150,
divide both sides by 60,
this would be x equals,
these two share a common factor of 30,
which would simplify to 5/2, or 2 1/2 or 2.5.
So x is equal to 2.5,
which means 150 milligrams is equivalent to 2.5 grains,
which now we can substitute 2.5 grains here,
for 150 milligrams, and then solve the original proportion.
We're going to go ahead and rewrite this as
one grain to one tablet,
equals, again, 2.5 grains
to x tablets.
And now because we have the same units on top,
and the same units on the bottom,
we can cross multiply and solve for x.
So, one times x equals one times 2.5,
one times x is x, one times 2.5 is 2.5,
and therefore, if the order is 150 milligrams,
which is equivalent to 2.5 grains,
then you will have to give the patient 2.5 tablets.
I hope you found this helpful.