Sarin participates in school anniversary event part 14 (Math Question)

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The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presenting the Math Concept, Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids will learn how to  deal with Math Modeling, Problem Sum from Lower Primary School to Upper Primary School level after reading the blog postings. This posting is an upper primary school math question on Ratio and Problem Sum.

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

  More Questions on Problem Solving. Click here….

More Questions on Ratio. Click here….

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