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 no none of the three.

How many are interested in exactly one kind of show?

Answer 1

Wheres the extra 14 people at?

Answer 2

those numbers don't even add up to 350

Answer 3

@tygrr321

Answer 4

yes

Answer 5

I really need help

Answer 6

ill try

Answer 7

thanks

Answer 8

gtg but know how to help

Answer 9

@Directrix

Answer 10

SORT THE SHOWS THEN ADD THE PEOPLE UP

Answer 11

I don't get it.

Answer 12

21 were interested in an interview show and reruns
14 were interested in an interview show and reruns but not a documentary

These two lines tell you two things:
(1) Exactly 21-14=7 were interested in all three types of show.
(2) We can count on statements that "N were interested in X and Y" to include those interested in all three, as well as those not interested in the third type. This gives us a method of calculating the totals for different possible groups.

We know how many were interested in 0 kinds of show (28).
We know how many were interested in 3 kinds of show (7).

For people interested in 2 kinds of show, there are three combinations:

(1) interview show and reruns, but not documentary (14, given).

(2) documentary and reruns but not interview show:
35 - 7 = 28 (because we have to exclude those interested in all three).

(3) interview show and documentary but not reruns (105, given)

That gives 14 + 28 + 105 = 147 interested in exactly 2 kinds of shows.

Subtracting all those who were interested in 0, 2, or 3 kinds of shows gives the number of respondents interested in exactly one kind:
350 - (28+7+147) = 350 - 182 = 168

Answer 13

that's what I found but idk how