2. To find the total quantity of a mixture when
the percentage strength and the amount of
the active ingredient are known, divide the
weight or volume of the active ingredient by the
percent (expressed as a decimal fraction).
3. To find the percentage strength when the
amount of the active ingredient and the total
quantity of the mixture are known, divide the
weight or volume of the active ingredient by the
total weight or volume of the mixture. Then
multiply the resulting answer by 100 to convert
the decimal fraction to percent.
ALTERNATE METHODS FOR SOLVING
PERCENTAGE PROBLEMS
The alternate method for solving percentage
problems, illustrated below, incorporates the three
rules discussed above into one equation. This method
is often preferred since it eliminates errors that may
result from misinterpreting the values given in the
problem.
% strength = Amt of active ingredient x 100(%)
Total amt of preparation
A variation of the alternate percentage equation,
illustrated below, uses “parts per hundred” instead of
percent, with X used as the unknown.
Amt of active ingredient = Parts of active ingredient
Amt of total preparation
100 parts (total mixture)
RATIO AND PROPORTION
CALCULATIONS
Ratio is the relationship of one quantity to another
quantity of like value. Example ratios are 5:2, 4:1.
These ratios are expressed as “5 to 2” and “4 to 1,”
respectively. A ratio can exist only between values of
the same kind, as the ratio of percent to percent, grams
to grams, dollars to dollars.
In other words, the
denominator must be constant.
6-14
Example: If a mixture contains 20% of substance Y,
how many grams of the 20% mixture would contain 8 g
of Y?
Solution: 20% is expressed as a decimal fraction
(0.20). Divide the weight (8 g) by the percent, thus:
40.0 g ,
the weight of 20%
.20 ) 8.00
mixture that would
8 0
contain 8 g of
00
substance Y.
Example: Find the percentage strength of Z if 300 g
of a mixture contains 90 g of substance Z.
Solution:
0.3 g ,
is the percent of Z
300 ) 90.00
expressed as a decimal
90
fraction
00
0.3 x 100(%) = 30% of Z in the mixture
Example #2: Calculate the amount of active ingredient
in 300 g of a 5% mixture of active ingredient B.
Solution: Convert 5% to a decimal fraction (0.05).
Substitute the known values in the equations, and use X
for the amount of the unknown ingredient .
0.05 = X/300
X = 15 g
Example #1: Calculate the percent of A in a solution if
120 g of that solution contains 6 g of A.
Solution: Substitute the known values in the equation
and use X for the percent (the unknown factor).
X = 6/120 x 100(%) = 5 (%)
Therefore, X = 5, which is the percent strength of the
solution.
Example: Ascertain the percent B in a mixture of
600 g that contains 15 g of B.
Solution:
=
X = 2.5, the parts of active ingredient
per 100 parts of total mixture, or
2.5%
15
600
=
X
100
600 X = 1500
X =
1500
600
