*Given
Percent of the wolves which are female - 55%
Percent of the wolves which hunt
in medium-sized packs - 20%
Percent of the wolves which are both
female and hunt in medium-sized
packs - 15%
*Solution
Assuming that there is a total of one hundred wolves in the species,
1. Since percent (%) means "per 100" or "for every 100" then,
a. The number of female wolves is
(55 female wolves / 100 wolves) * 100 wolves total = 55 female wolves
b. The number of wolves that hunt in medium-sized packs is
(20 wolves / 100 wolves) * 100 wolves total = 20 wolves
Note that the 20 wolves is a mixture of male and female wolves.
c. The number of female wolves that hunt in medium-sized packs is
(15 female wolves / 100 wolves) * 100 wolves total = 15 female wolves
2. Because there is a total of 55 female wolves in the species, and 15 of these wolves hunt in medium-sized packs, then the number of female wolves that do not hunt in medium-sized packs is,
55 female wolves total - 15 female wolves hunting = 40 female wolves not
in medium-sized packs hunting in medium
sized packs
3. To find the proportion, we can express the answer in terms of percent (%) or in fraction, which is usually how proportions are expressed.
For every 100 wolves, there are 40 female wolves that do not hunt in medium-sized packs. This can be expressed as a proportion of
40
100
and simplified by dividing both the numerator and denominator by 10, we get,
40/10
100/10
4
10
When this is expressed in percent, we multiply the fraction or proportion by 100% to get,
4 x 100% = 40%
10
Thus, the proportion of female wolves that do not hunt in medium sized packs is 4/10 or 0.4. When expressed as percent, this is 40%.