### Sample Problem

The number of students in Class A, B and C is in the ratio of 4:6:5. There are 12 more students in Class B than in Class A.

(a) How many students each are there in Class A, B and C?

Class A: students

Class B: students

Class C: students

(b) If there are 6 students in each row of Class C, how many rows are there in Class C?

rows

#### Solution

(a)

Solution 1:

Set the number of students in Class A as 4 units, in Class B as 6 units and in Class C as 5 units. So, the difference between Class A and Class B is (6 – 4 = 2) units. Then,

2 units = 12

1 unit = 12 ÷ 2 = 6

Class A: 4 units = 4 × 6 = 24

Class B: 6 units = 6 × 6 = 36

Class C: 5 units = 5 × 6 = 30

Solution 2:

Use the method of finding an equivalent ratio to find the number of each part parts.

A : B : (B –A) : C

4 : 6 : (6 – 4 = 2) : 5

4 × a : 6 × a : (2 × a = 12) : 5 × a

From the chart above we know that, a = 12 ÷ 2 = 6

So,

Class A: 4 × a = 4 × 6 = 24

Class B: 6 × a = 6 × 6 = 36

Class C: 5 × a = 5 × 6 = 30

(b)

30 ÷ 6 = 5

There are 5 rows in Class C.