shanice wrote:In a recent anonymous poll of a certain private community, 22 percent of its 2500 residents reported that they were suffering from depression. Of this group of depressed people, 20 percent were at least sixty years old. If 25 percent of all the people are at least sixty years old, how many people over the age of sixty did not report that they were suffering from depression?
This is an EITHER/OR group question.
Every resident EITHER suffers from depression OR does not.
Every resident EITHER is at least 60 years old OR is not.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.
Let D = depressed, ND = not depressed.
Here's the grid, with the following percentages inserted:
Total = 100.
Total D = 22.
D + at least sixty years old = .2(22) = 4.4.
Total at least 60 = 25.
_______________D________ND_______Total
≥60:__________4.4_________________25
<60:________________________________
total:__________22_________________100
The values in each row and column must add up to the total.
Thus, ND + at least 60 = 20.6%:
_______________D______ND_______Total
≥60:__________4.4____20.6________25
<60:________________________________
total:__________22________________100
Thus, 20.6% of the 2500 people are not depressed and at least 60:
.206(2500) = 515.
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