Handshakes

A group of 200 high school students, 105 girls and 95 boys, is randomly divided into two rows of 100 students each. Each student in one row is directly opposite a student in the other row, and all the opposite pairs of students shake hands. Prove that the number of girl-girl handshakes is 5 more than the number of boy-boy handshakes.
Source: NCTM Mathematics Teacher 2008

SOLUTION
Let bb be the number of boy-boy handshakes; gg the number of girl-girl handshakes; bg the number of boy-girl handshakes.
2bb+bg=95
2gg+bg=105
95-2bb=105-2gg
2gg-2bb=10
gg-bb=5
gg=bb+5
The number of girl-girl handshakes is 5 more than the number of boy-boy handshakes.

Answer: Given in solution

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About mvtrinh

Retired high school math teacher.
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