有幾條maths唔識...

1.
Number of people:2 ; number of handshakes: 1 = 1(2)/2
Number of people:3 ; number of handshakes: 1 + 2 (The new comer shakes hands with the two people, each once) = 2(3) / 2

Similarly, we have:
Number of people:4 ; number of handshakes: 1 + 2 + 3 = 3(4)/2
Number of people:5 ; number of handshakes: 1 + 2 + 3 + 4 =4(5)/2
Number of people:n ; number of handshakes: 1 + 2 + 3 + ... + (n - 1) =n(n - 1)/2

The number is given by the formula: n(n -1)/2:
Let n be the number of people in the party.
n(n-1)/2 = 780
n^2 - n - 1560 = 0
(n + 39)(n - 40) = 0
n = -39(rejected) or n=40

There were 40 people in the party.

2.
Let xm be the width of the pathway.
(36 + 2x)(45 + 2x) = 2332
1620 + 72x + 90x + 4x^2 = 2332
4x^2 + 162x - 712 = 0
2x^2 + 81x - 356 = 0
(2x + 89)(x - 4) = 0
x = -89/2 (rejected) or x=4

The width of the pathway is 4m

1. 780/3 = 260(people)

2. 45*36+x=2332
1620+x=2332
x=2332-1620
x=508
..............
you must find out it yourself!

1.你話each person shook handS,即係每一個人揮兩隻手,因為有"s"
答案應該係780/2=390.

2. area of flowerbed= 36x45=1620m^2
area of pathway =2332-1620=712m^2
ans: width of pathway= 712開方=26.68m