It was once said that Country-Western songs emphasize
three basic themes: love, prison, and trucks. A survey of the local Country-
Western radio station produced the following data:
12 songs about a truck driver who is in love while in prison
13 about a prisoner in love
28 about a person in love
18 about a truck driver in love
3 about a truck driver in prison who is not in love
2 about people in prison who are not in love and do not drive trucks
8 about people who are out of prison, are not in love, and do not drive trucks
16 about truck drivers who are not in prison
(a) How many songs were surveyed?
Find the number of songs about:
(b) truck drivers
(c) prisoners
(d) truck drivers in prison
(e) people not in prison
(f) people not in love
no
(a) To find the total number of songs surveyed, we need to add up the number of songs for each category:
12 + 13 + 28 + 18 + 3 + 2 + 8 + 16 = 100
So, 100 songs were surveyed.
(b) The number of songs about truck drivers is the sum of songs that mention truck drivers in any context:
12 + 18 + 3 + 16 = 49
There were 49 songs about truck drivers.
(c) The number of songs about prisoners is the sum of songs that mention prisoners in any context:
13 + 3 + 2 = 18
There were 18 songs about prisoners.
(d) The number of songs about truck drivers in prison who are in love is given:
12
There were 12 songs about truck drivers in prison.
(e) The number of people not in prison is the sum of songs that mention people who are out of prison, not in love, and do not drive trucks:
8
There were 8 songs about people not in prison.
(f) The number of songs about people not in love is the sum of songs that mention people who are out of prison, not in love, and do not drive trucks:
8
There were 8 songs about people not in love.
(a) To find the total number of songs surveyed, we need to add up the given data. Adding all the numbers together:
12 + 13 + 28 + 18 + 3 + 2 + 8 + 16 = 100
Therefore, a total of 100 songs were surveyed.
(b) The number of songs about truck drivers can be found by adding the songs that mention truck drivers, regardless of their love or prison status:
12 (truck driver in love while in prison) + 18 (truck driver in love) + 16 (truck driver not in prison) = 46
Therefore, there were 46 songs about truck drivers.
(c) The number of songs about prisoners can be found by adding the songs that mention prisoners, regardless of their love or truck driving status:
13 (prisoner in love) + 3 (truck driver in prison who is not in love) + 2 (people in prison who are not in love and do not drive trucks) = 18
Therefore, there were 18 songs about prisoners.
(d) The number of songs about truck drivers in prison can be found by looking at the specific mention of truck drivers in prison:
12 (truck driver in love while in prison) + 3 (truck driver in prison who is not in love) = 15
Therefore, there were 15 songs about truck drivers in prison.
(e) The number of songs about people not in prison can be found by subtracting the songs about prisoners from the total number of songs surveyed:
100 (total songs) - 18 (songs about prisoners) = 82
Therefore, there were 82 songs about people not in prison.
(f) The number of songs about people not in love can be found by adding the songs that mention people who are out of prison, not in love, and do not drive trucks:
8 (people out of prison, not in love, and do not drive trucks) + 2 (people in prison who are not in love and do not drive trucks) = 10
Therefore, there were 10 songs about people not in love.