Form 2 maths (Rate and Ratio)急

1. If 2a + b = 6a - 5b, find a : b.

2a + b = 6a - 5b
b + 5b = 6a - 2a
6b = 4a
2a = 3b
a/b = 3/ 2
a : b = 3 : 2


2. Given 2 numbers a and b. If 3a - 4b = 0 and their sum is 84
(a)Find the radio a: b.
(b)Find the values of a and b.

(a)
3a - 4b = 0
3a = 4b
a/b = 4/ 3
a : b = 4 : 3

(b)
a : b = 4 : 3
Let a = 4k and b = 3k

a + b = 84
4k + 3k = 84
7k = 84
k = 12

a = 4 x 12
Hence, a = 48
b = 3 x 12
Hence, b = 36


3. In May 4 days were cloudy. The number of rainy days was 3 more than the number of sunny days.
(a) How many days were sunny?
(b) Find the radio of the number of rainy days to the number of sunny days.

(a)
No. of days in May = 31 days
No. of cloudy day = 4 days

Let n be the number of sunny days in May.
Then, the number of rainy days in May = 31 - (4 + n) = (27 - n) days

(Number of rainy days) = (Number of sunny day) + 3
27 - n = n + 3
2n = 24
n = 12
Number of sunny day = 12 days

(b)
Number of rainy days = (12 + 3) days = 15 days

(Number of rainy days) : (Number of sunny days)
= 15 : 12
= 5 : 4