Overlapping Sets?

[cssears]

Is there a way to use a double set matrix for this problem?

In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all hte employees are at least 35 years old, what fraction of the employees in the corporation are female?

3/5
2/3
3/4
4/5
5/6

[nav.adi]

Yes this problem can be solved using the double set matrix method--

The matrix would be set as follows--

Columns-- Age (>=35 and <35)
Rows -- Male/Female
Total count(Male + Female)= 100 (assumption)

Given that
>= 35 (Male)= 0.50 x, where x is the total number of males
>=35 (Female)= 0.40 y, where y is the total number of females

.42(x+y) = .50x + .40y, where (x + y) = 100
.42*100 = .50x + .40y ---- eq 1
100 = x+y ------------------eq 2

So now you have two equations and you can solve for x and y

y would be 80, but remember that the question asks us for the fraction, therefore the answer would be
80/100 = 4/5

Hope this helps!!!

[mschwrtz]

Good set up. Notice that the columns are always divided according to some yes-or-no question. That is, every member of the largest group is in exactly one of the two columns. Same thing with the rows.

If a problem stipulates that every member of the Foreign Language Club speaks Spanish or French, and that no member speaks both, the Spanish/French just means Spanish/not Spanish, so Spanish/French is a Y/N question. So the columns could be Spanish/French and the rows...well, depends on the problem...male/female (on the assumption that everyone is one or the other and nobody is both), adult/child (on the assumption that everyone is one or the other and nobody is both), etc.

On the other hand, if a problem doesn't stipulate that BOTH THAT every member of the Foreign Language Club speaks Spanish or French, AND THAT no member speaks both, then the columns might be Spanish/not Spanish and the rows might be French/not French.