The museum's show for July features 30 oil paintings by different artists. All artists show the same number of paintings, and each artist shows more than one painting. How many artists could be featured in the show?

The possible numbers of artists that could appear in the show are 2, 3, 5, 6, 10, and 15. Each of these numbers represents a situation where the 30 paintings can be evenly distributed among the artists, and each artist has more than one painting. ;

Answered by JunoTemple | 2024-06-18

Answer: We have many options:

15 artists, with 2 paintings per artist.
10 artists, with 3 paintings per artist.
6 artists, with 5 paintings per artist.
5 artists, with 6 paintings per artist.
3 artists, with 10 paintings per artist.
2 artists, with 15 paintings per artist.

by different artists, then the number of artists must be more than 1. each artist shows more than 1 painting: >1 painting/artist
(30 oil paintings)/(2 paintings/artist)=15 artists (30 oil paintings)/(3 paintings/artist)=10 artists (30 oil paintings)/(5 paintings/artist)=6 artists (30 oil paintings)/(6 paintings/artist)=5 artists (30 oil paintings)/(10 paintings/artist)=3 artists (30 oil paintings)/(15 paintings/artist)=2 artists

Answered by Professor1994 | 2024-06-24

The number of artists featured in the show can vary depending on how many paintings each artist exhibits. Possible numbers of artists that could be featured are 15, 10, 6, 5, 3, or 2. Each artist must show more than one painting, thus determining these combinations.
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Answered by Professor1994 | 2024-09-30