Question

A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 350 responses with the following results:

105 were interested in an interview show and a documentary, but not reruns
14 were interested in an interview show and reruns but not a documentary
49 were interested in reruns but not an interview show
84 were interested in an interview show but not a documentary
35 were interested in a documentary and reruns
21 were interested in an interview show and reruns
28 were interested in none of the three

How many are interested in exactly one kind of show?

Answer 1

@narissa

Answer 2

You just need to read and do basic addition to get the answer.

Answer 3

Hints:
First line: the respondent was interested in 2 kinds of shows: interview and doc.
Second lilne: the respondent was int. in interview and reruns.
Keep going through the list until you find the line that more or less says that the respondent is interested in only one kind of show.

Answer 4

Hints:
This is basically a Venn diagram problem.
1. If three options (Interview, documentary and reruns) are involved, you need to draw three intersecting circles, one for each, like shown below:

2. The rectangle represents all 350 respondants.
3. Each respondant must be placed in exactly one place. For example, 28 were interested in none of the three, so they will be placed outside all the circles, but inside the rectangle.

Answer 5

Then you would look for the number that is interested in all three, which is NOT given. This would have been the easiest starting point (area E below).
Lacking the area E, we would label all the areas and formulate equations according to the given information.
A possible way to assign names could be the following:

Then proceed to write equations as per given information.
"105 were insterested in Interview and Documentary, but not reruns" translates to
A+B+C=105 (but not D, E and F because they belong to reruns).
and so on.
As you go on, you will find that there are two conflicting statements, which should prompt you to review for typos.
Hint: lines related to 14 and 84.
So after correcting the typo(s), you can continue forming the equations, and eventually solve them (variables A-G).