Ratio and Rate

1.A post is painted in black and white in the ratio of 3:2. If the length of the white portion is 4m, find the length of the post.

4/(2/(3+2))
=10m//

The length of a wire is 360cm. If it is divided into 3 portions in the ratio of 1:3:8, find the length of the longest portion

360 x 8/(1+3+8)
=240cm//


Given that x+y =39 and x:y = 4:9.
a) For the expression x:y = 4:9, express x in terms of y.
x+y=39
x=39-y--(1)
x:y=4:9
x/y=4/9
9x=4y
9(39-y)=4y
351-9y=4y
351=13y
y=27//

x=39-y
=39-27
=12//
so x=12 and y=27
Let the length of the black portion be y m.
y:4=3:2
2y=12
y=6
Therefore the length of the black portion is 6 m.
Therefore the length of the post is 4+6=10 m.


2.
The length of the longest portion
=360x8/(1+3+8)
=360x8/12
=240 (cm)
(3)
(a)
x=39-y---(*)
(b)
x:y=4:9
(39-y):y=4:9
9(39-y)=4y
351-9y=4y
13y=351
y=27---(**)
Sub (**) into (*)
x=39-y
=39-27
=12
2.

1. A post is painted in black and white in the ratio of 3:2. If the length of the white portion is 4m, find the length of the post.

4/(2/(3+2))
=10m//

2. The length of a wire is 360cm. If it is divided into 3 portions in the ratio of 1:3:8, find the length of the longest portion

360 x 8/(1+3+8)
=240cm//


3. Given that x+y =39 and x:y = 4:9.
a) For the expression x:y = 4:9, express x in terms of y.
x+y=39
x=39-y--(1)
x:y=4:9
x/y=4/9
9x=4y
9(39-y)=4y
351-9y=4y
351=13y
y=27//

x=39-y
=39-27
=12//
so x=12 and y=27

(1)
Let the length of the black portion be y m.
y:4=3:2
2y=12
y=6
Therefore the length of the black portion is 6 m.
Therefore the length of the post is 4+6=10 m.
(2)
The length of the longest portion
=360x8/(1+3+8)
=360x8/12
=240 (cm)
(3)
(a)
x=39-y---(*)
(b)
x:y=4:9
(39-y):y=4:9
9(39-y)=4y
351-9y=4y
13y=351
y=27---(**)
Sub (**) into (*)
x=39-y
=39-27
=12