Percentage problem

I need help with the following percentage question:


In a 400-people population, it has been done examinations to diagnose anemia and intestinal parasitism. The results made it clear that:

- 80% of the people with anemia have also intestinal parasitism;

- 50% of the people with intestinal parasitism have also anemia;

- 220 people have neither anemia nor intestinal parasitism.

Out of the 400 people, what is the percentage of people with anemia?


I know that the answer is 25%, but how do I get at it?

Quote:

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Originally Posted by nvwxgn

I need help with the following percentage question:


In a 400-people population, it has been done examinations to diagnose anemia and intestinal parasitism. The results made it clear that:

- 80% of the people with anemia have also intestinal parasitism;

- 50% of the people with intestinal parasitism have also anemia;

- 220 people have neither anemia nor intestinal parasitism.

Out of the 400 people, what is the percentage of people with anemia?


I know that the answer is 25%, but how do I get at it?

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You must start defining.

A = # of folks with anemia
P = # of folks with parasites
B = # of folks with both
220 = # of folks with neither

We have immediately:

1) A + P - B = 400-220 = 180
2) A(0.80) = B
3) P(0.50) = B

Solving - Substitute 2) and 3) into 1)

(b/(0.8) + B/(0.5) - B) = 180 ==> B = 80

Back-Substitute into 2)

A = 80/(0.8) = 100

Answer: 100/400 = 0.25

Note: I did not see how to solve this problem until AFTER I wrote clear and sufficient definitions. Only after those four rows did I see where this was going and that the information given was sufficient.

Note: Notice how I did NOT solve for P. P was not the most convenient first solution (B) and P was not the item asked for (A). Again, the defintions, clear and sufficient, made it possible to know what to go for first.

you can also do this with just one varible

let A = people with anemia

since half the people with intestinal parasitism have A and those with A .8 have intestinal parasitism

then

so

and

I should mention that I also drew a diagram of what was going on... then it all came down to something
obviously simple. word problems really need to be transformed into a way that is clear what is happening

Good. Thanks a lot