Ratios
TWO SETS OF RATIOS AND 3 OBJECTS/ITEMS
One type of question has 2 sets of ratios and 3 items/objects. One of the objects is the common item in the 2 sets of ratio.
Solve the question by using common item to ‘link’ the two sets of ratio.
Example:
The ratio of the number of oranges to apples is 2:5 and the ratio of the number of oranges to pears is 6:7. What is the ratio of the number of orange to apples to pears?
Method
Step1: Write the sets of ratio side by side
O A O P
2 5 6 7
Step2: Identify common item (Orange)?
Put the common item of the ratio in the middle
A O
5 2
O P
6 7
Step3: Find/Draw Common Multiple in-line and ‘equal’ the common item value
(Common multiple for 2 and 6 is 6)
A O
5x 3 2x 3
O P
6 7
A O P
15 6 7
Step4: Solve question to the sequence required
(It is orange to apples to pears.)
The ratio of the number of orange to apples to pears is 6:15:7
Note: The sequence of the ratios relative to the items must be maintained.
Example
Ali and Billy had a number of marbles in the ratio of 2:7. Ali and Cecil had a number of marbles in the ratio of 3:1. It they had a total of 168 marbles altogether, how many more marbles did Billy have than Cecil?
Method
Step1: Write the sets of Ratio side by side
A B A C
2 7 3 1
Step2: Who is common, Ali)?
Draw/Put the common item of the ratio in the middle
B A
7 2
A C
3 1
Step3: Find the common multiple and ‘equal’ the common item value
(Common multiple for 2 and 3 is 6)
B A
7x3 2x3
A C
3x2 1x2
Step4: Solve question to the sequence required
B A
21 6
A C
6 2
B A C
21 6 2
Total = 21 + 6 + 2 = 28u
28 u = 168, u = 6
Cecil has 2 x 6 = 12 cards, Billy has 21 x 6 = 126 cards
Billy has 126 – 12 = 114 cards more than Cecil.
