bharath539 wrote:
In a certain senior class, 72 percent of male students and 80 percent of the female students have applied to college. What fraction of the senior class are male?
1)There are 840 students in the senior class.
2)75 percent of the senior class have applied to college.
Sure! Let's start by breaking down the question stem.
We know that 72% of males and 80% of females have applied to college. We want to know that percent of the entire class is male.
We think: lots of missing information; since the question is asking us for a percent, not an actual number, we may be able to solve without any actual numbers.
To the statements:
(1) total number of students. However, we don't know anything more about the breakdown, so no way to figure out what percent is male: insufficient.
(2) 75% of all seniors applied to college.
Well, we know the percents for the males and the females. Therefore, if we know the total percent, we can figure out the weighting of the two groups: sufficient.
If we actually needed to solve, we could use the weighted average formula:
72%(m) + 80%(f) = 75%(m+f)
multiplying both sides by 100 to eliminate percents:
72m + 80f = 75m + 75f
5f = 3m
5/3 = m/f
if the ratio of males:females is 5:3, then 5 out of every 8 students is male, i.e. 5/8 or 62.5% of the class must be male.
We could also solve by plotting the info on the number line and using a simple rule:
72 -------75------------80
calculate the distances between each group and the total average:
72---3----75----5------80
Here's the rule: the ratio of weights is the inverse of the ratios of the distances.
In other words, the ratio of the 72 group to the 80 group is the inverse of 3 to 5, or 5 to 3.
Abstractly:
Group 1 average---------x------------overall average---------y----------Group 2 average
Group 1:Group 2 = y:x
