The ratio of the number of pupils in Class A to the number of pupils in Class B is 2:5. The ratio of the pupils in Class B to the number of pupils in Class C is 10:3.
a. Find the ratio of the number of pupils in Class A to the number of pupils in Class B to the number of pupils in Class C.
b. If there are 70 pupils in Class A and Class C altogether, how many pupils are there in Class B?
c. If Class B has 40 pupils, how many pupils are there in Class A and Class C altogether?
A : B = 2 : 5 or 4 : 10 (looking at the next line)
B : C = 10 : 3
so A : B : C = 4 : 10 : 3
b)
A : C = 10 : 3
so 3A = 10C ---> A = 10C/3
also A+C = 70
12C/3 + C = 70
12C + 3C = 210
15C = 210
C = 14
B = 56
c) I assume we go back to the original definition, and the count is different from b)
A : B : C = 4:10:3
A:40:C = 4:10:3 = 16:40:12
Then A 16 , C=12
A+C = 28
To solve these types of problems, we can use proportional reasoning and set up ratios based on the given information.
a. To find the ratio of the number of pupils in Class A to the number of pupils in Class B to the number of pupils in Class C, we will combine the given ratios.
Given ratio for Class A to Class B: 2:5
Given ratio for Class B to Class C: 10:3
To combine these ratios, we need to determine a common term between Class B in the first ratio and Class B in the second ratio.
Since the first ratio is Class A to Class B, and the second ratio is Class B to Class C, we can rewrite the first ratio as Class A to Class B to Class C. To do this, we need to multiply the second ratio by the number of pupils in Class B from the first ratio.
Given ratio for Class B to Class C: 10:3
Number of pupils in Class B in the first ratio: 5
Multiply the second ratio (Class B to Class C) by the number of pupils in Class B from the first ratio: 5 × (10:3) = 50:15
The new combined ratio is:
Class A to Class B to Class C = 2:5:15
b. If there are 70 pupils in Class A and Class C altogether, we can use the ratio from part a to find the number of pupils in Class B.
Given ratio for Class A to Class B to Class C: 2:5:15
Number of pupils in Class A: 70
To find the number of pupils in Class B, multiply the number of pupils in Class A by the ratio of Class B to Class A:
Number of pupils in Class B = (70 × 5) / 2 = 35 × 5 / 2 = 175 / 2 = 87.5
Therefore, there are 87.5 pupils in Class B. Since we cannot have a fraction of a person, we need to round it to the nearest whole number. Thus, there are 88 pupils in Class B.
c. If there are 40 pupils in Class B, we can again use the ratio from part a to find the number of pupils in Class A and Class C altogether.
Given ratio for Class A to Class B to Class C: 2:5:15
Number of pupils in Class B: 40
To find the number of pupils in Class A and Class C, multiply the number of pupils in Class B by the ratio of Class A to Class B to Class C:
Number of pupils in Class A and Class C = (40 × 2) / 5 = 80 / 5 = 16
Therefore, there are 16 pupils in Class A and Class C altogether.