Problem: At a dance party a group of boys and girls exchange dances as follows: one boy dances with 5 girls, a second boy dances with 6 girls, and so on, the last boy dancing with all the girls. If b represents the number of boys and g , the number of girls, then:
Answer Choices:
A. b=g
B. b=g/5
C. b=g−4
D. b=g−5
E. It is impossi- ble to determine a relation between b and g without knowing the total number of boys and girls.
Solution:
Set up the following table, a one-to-one cuirespondence between the elements of the boy set and the girl set:
Boy number Girls danced with ​15​26​37​……​bb+4​
therefore g=b+4 ; b=g−4
5,6,7,…,g
1=a+(n−1)d
g=5+(b−1)(1);b=g−4