Respuesta :
Answer:
There are 8 teams that have nicknames without a color and don't end in "s.
Step-by-step explanation:
This can be solved by treating each value as a set, and building the Venn Diagram of this.
-I am going to say that set A are the teams that have nicknames that end in S.
-Set B are those whose nicknames involve a color.
-Set C are those who have nicknames without a color and don't end in "s.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a are those that have nickname ending in "s", but no color, and [tex]A \cap B[/tex] are those whose nickname involves a color and and in "s".
By the same logic, we have
[tex]B = b + (A \cap B)[/tex]
In which b are those that nicknames involves a color but does not end in s.
We have the following subsets:
[tex]a,b, (A \cap B), C[/tex]
There are 129 schools, so:
[tex]a + b + (A \cap B) + C = 129[/tex]
Lets find the values, starting from the intersection.
The problem states that:
13 nicknames involve both a color and end in "s". So:
[tex]A \cap B = 13[/tex]
19 have nicknames that involve a color. So:
[tex]B = 19[/tex]
[tex]B = b + (A \cap B)[/tex]
[tex]b + 13 = 19[/tex]
[tex]b = 6[/tex]
115 have nicknames that end in "s". So:
[tex]A = 115[/tex]
[tex]A = a + (A \cap B)[/tex]
[tex]a + 13 = 115[/tex]
[tex]a = 102[/tex]
Now, we just have to find the value of C, in the following equation:
[tex]a + b + (A \cap B) + C = 129[/tex]
[tex]102 + 6 + 13 + C = 129[/tex]
[tex]C = 129 - 121[/tex]
[tex]C = 8[/tex]
There are 8 teams that have nicknames without a color and don't end in "s.
