Whole Number P5

8. A group of people met at a party. Each person shook hands with everyone else. Mr Li shook hands with 3 times as many men as women. Mrs Li shook hands with 4 times as many men as women. How many men and how many women were there at the party?

Mr Li             

     [     ]1[     ]1[     ]11

M   [       ][       ][      ]1

W   [       ]

Mrs Li

M   [     ][     ][     ][     ]

W   [     ]1

4 u -- > 3 u + 1 x 4

1 u -- > 4

M -- > 4 x 4 = 16 men

W -- > 4 + 1 = 5 women

There were 16 men and 5 women at the party.