The local Jazz Club met 50 times last year. At each meeting there were 20 slots on the playlist, with one tune played in each slot. A careful study of the playlists for last year showed that: 40% of the slots were used for tunes that were not played at any other time that year. 45% of the slots were used for tunes that were played just twice. Half of the remaining slots were used for tunes that were played 3 times. There were only 5 other tunes played during the year, and the number of times that these were played was in the ratio 5 : 4 : 3 : 2 : 1. How many different tunes will a member who attended all meetings have heard during the year?
A655
B 705
C 880
D 930

The total number of different tunes will a member who attended all meetings have heard during the year is 655 and this can be determined by using the given data.

Given :

The local Jazz Club met 50 times last year. At each meeting there were 20 slots on the playlist, with one tune played in each slot.
A careful study of the playlists for last year showed that: 40% of the slots were used for tunes that were not played at any other time that year.
45% of the slots were used for tunes that were played just twice.
Half of the remaining slots were used for tunes that were played 3 times.
There were only 5 other tunes played during the year, and the number of times that these were played was in the ratio (5 : 4 : 3 : 2 : 1).

The total number of slots is given by:

[tex]50\times 20 = 1000[/tex]

So, the total number of tunes in each slot is 1000.

The total number of remaining tunes is given by:

[tex]=1000-(400+450)[/tex]

= 150

According to the given data half of the remaining tunes were played thrice that is 75 tunes were played thrice and only 5 other tunes were played out of the remaining 75 tunes.

So, the total number of tunes a member will hear is given by:

[tex]=400+\dfrac{450}{2}+\dfrac{75}{3}+5[/tex]

= 655

So, the total number of different tunes will a member who attended all meetings have heard during the year is 655.

For more information, refer to the link given below:

https://brainly.com/question/23017717