未知數、比

1.已知A,B,C三人以7:4:5的比來分一筆$640的錢,他們各分得多少?
設A,B,C三人各有$7k, $4k, $5k
7k + 4k + 5k = 640
16k = 640
k = 40
A分得 = 7*40 = $280
B分得 = 4*40 = $160
C分得 = 5*40 = $200

2.偉峰和是志毅二人身高的比是8:9.若偉峰的身高是160cm,志毅的身高是多少?
設偉峰的身高為8k cm, 志毅身高為9k cm
8k = 160
k = 20
志毅身高 = 9*20 = 180cm

3(a). (x+2):x=3:2
(x+2) / x = 3 / 2
2(x+2) = 3x
2x + 4 = 3x
x = 4
3(b). y:5=(y-6):3
y / 5 = (y-6) / 3
3y = 5(y-6)
3y = 5y - 30
-2y = -30
y = 15

展開
(x-5)(x+5) = x^2 - 5^2 = x^2 - 25
(-x+6)(-x-6) = (-x)^2 - 6^2 = x^2 - 36
(3y+2)(3y-2) = (3y)^2 - 2^2 = 9y^2 - 4
(5y-8x)(5y+8x) = (5y)^2 - (8x)^2 = 25y^2 - 64x^2
試不使用計算機,計算下列的值
155^2-145^2
= (155+145)(155-145)
= 300*10
= 3000