Direct proportion
Two quantities are said to be in direct proportion if they increase or decrease at the same rate.
The ration between two corresponding values in the two quantities is the same.
Example
In a school, 4 teachers serves 80 students.
(a) how many teachers will be needed for 150 students.
(b) what number of students can be served by 6 teachers.
(a)Solution
The number of students increases by ratio:
150:80=15:8
The number of teachers will increase in the same ratio.
Hence (15/8)*4=approximate 8 teachers. The correct answer from the working is 7.5 but we approximate to the nearest whole number because we cannot have fractional number of teachers.
(b) solution
Teachers has increase by the ration 6:4=3:2
Increase the number of teacher by the same ration:
(3/2)*80= 120 students
Inverse proportion
Two quantities are inversely proportional to each other if increase of one quantity causes decrease of the other quality by the same ratio and decrease of one quantity results to increase of the other quantity.
Example
A farmer has enough feed to last her 75 vows for 30 days. If he buys 15 more cows, how long will the feed last now?
Solution
cows increases in the ratio 90:75= 6:5
The feed days decreases by the ratio 5:6, hence, the feed will be used in (5/6)*30=25.
Meaning if cows increases by 15 based on the current stock value, the feed stock will last 5 days less