SOLUTION: There are 10 students on the volleyball team and 15 on the basketball team. When planning a field trip with both teams, the coach has to arrange transportation for a total of only

Click here to see ALL problems on Probability-and-statistics

Question 1201505: There are 10 students on the volleyball team and 15 on the basketball team. When planning a field trip with both teams, the coach has to arrange transportation for a total of only 19 students.
a) Use a Venn Diagram to illustrate this situation.
b) Determine how many students are on both teams.
c) How many students are only in volleyball team?
d) How many students are only in basketball team?
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

Venn Diagram template:

region a = volleyball only
region b = both sports
region c = basketball only
region d = neither sport mentioned

I'll assume that d = 0, i.e. all of the players mentioned play either sport or both.

total = (number who play volleyball)+(number who play basketball) - (number who play both)
19 = (10)+(15) - (number who play both)
19 = 25 - (number who play both)
number who play both = 25-19
number who play both = 6
This value goes in region b.

volleyball:
a+b = 10
a+6 = 10
a = 10-6
a = 4 who play volleyball only

basketball:
b+c = 15
6+c = 15
c = 15-6
c = 9 who play basketball only

This is what the completed Venn Diagram looks like