Question

# 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 girls. If b represents the number of boys and g the number of girls, then:

A
b=g
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B
b=g5
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C
b=g4
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D
b=g5
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E
It is impossible to determine a relation between b and g without knowing the total number of boys and girls
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Solution

## The correct option is C b=g−4Set up the following table, a one to tone correspondence between the elements of the boy set and the girl set:Boy number =1,2,3,...bGirl danced with =5,6,7,.....b+4;∴ g=b+4;b=g−4or the formula for the last term of the arithmetic sequence 5,6,7,....g; g=5+(b−1)(1);b=g−4

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