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Read the posting on **Sarin participates in school anniversary event part 1 **for story on school anniversary.

To read also the posting on **Sarin learns concept of ratio in school **to understand the concept of Ratio.

*Challenge yourself with the question before look out for the given solution‼*

**Upper primary school mathematics question UPQ271**

The member of Sarin’s team that taken care of the school anniversary dinner event was form by the pupil representatives from three different classes. Class A had 18 more representatives than Class B and 6 fewer representatives than Class C. The ratio of the number of boys to girls from the three schools was 1 : 3. The ratios of the number of boys to the number of girls in Class A, B and C were 1 : 3, 1 : 5 and 2 : 5 respectively. How many representatives from the three classes were there in all?

Solution:

Draw the model based on the number of representative different.

Take Class B as base line

Added the information of the ratio of the Boys and girls in each class to the model

The initial model

Proportion out the number of the green and yellow blocks based on the boys and girls ratio in each school

Ratio of Boys to Girls in Class A = 1 : 3

4 units = 18

Boys = 1 unit = 4 ½

Girls = 3 units = 27/2 = 13 ½

Ratio of boys to Girls in Class C = 2 : 5

7 units = 24

1 unit = 3 3/7

Boys = 2 units = 6 6/7

Girls = 5 units = 17 1/7

Normalise the number of units in all classes

Total number of units = 4 × 6 × 7 = 168 units

Porportion also the units to the number units and update the model

The updated model

From the updated model,

Total number of boys = 42U + 4 ½ + 28U + 48U + 6 6/7 = 118U + 11 5/14

Total number of girls = 126U + 13 ½ + 140U + 120U + 17 1/7 = 386U + 30 9/14

The overall boys to Girls ratio is 1 : 3

So 3 times of total number of boys = Total number of girls

3 times of total Boys = 3 × (118U + 11 5/14) = 354U + 34 1/14

Therefore

354U + 34 1/14 = 386U + 30 9/14

32U = 3 6/14 = 24/7

1U = 3/28

Total number of representatives from the three classes

= 118U + 11 5/14 + 386U + 30 9/14

= 504U + 42

= 504 × 3/28 + 42

= 54 + 42 = 96