A group of people met at a party. Each person shook hands with everyone else. Mr. smith shook hands with 3 times as many men as women. Mrs. smith shook hands with 4 times as many men as women.
How many men and women were there at the party?
thnks in advance " )
2007-03-15 22:50:44 · 4 answers · asked by pradaonly 1 in Science & Mathematics ➔ Mathematics
Mr Smith shook hands with 3 times as many men as women
Mrs Smith shook hands with 4 times as many men as women
This means that:
m = number of men at the party (including Mr Smith)
w = number of women at the party (including Mrs Smith)
(m - 1) = 3w
Note: m - 1 because Mr Smith didn't shake hands with himself
m = 4(w - 1)
Note: w - 1 because Mrs Smith didn't shake hands with herself
Solving these simultaneously
(4(w - 1) - 1) = 3w
4w - 4 - 1 = 3w
4w - 5 = 3w
w = 5
m = 4(w - 1)
m = 4(5 - 1)
m = 4(4)
m = 16
16 men and 5 women, including Mr and Mrs Smith.
2007-03-16 00:25:34 · answer #1 · answered by Tom :: Athier than Thou 6 · 0⤊ 0⤋
I came up with a total of 5 women and 16 men at the party. (Including Mr. and Mrs. Smith. They also shook hands with each other).
2007-03-16 06:20:08 · answer #2 · answered by quizkid 3 · 0⤊ 0⤋
16 men and 5 women
2007-03-16 06:04:12 · answer #3 · answered by David M 3 · 1⤊ 0⤋
16 men, 5 women
2007-03-16 09:37:45 · answer #4 · answered by u 2 · 0⤊ 0⤋