Sarin’s family attend concert at the Esplanade Part 16 (Math Question)

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

The story on Sarin’s family attend concert at the Esplanade you can read postings on Sarin’s family attend concert at the Esplanade in Welcome category and Sarin’s family attend concert at the Esplanade Part 2 (Math Question).

You should also click and read the posting on Sarin learns concept of ratio in school to understand mathematics concept of Ratio.

Read also the posting on Sarin learns Average Number, Percentage and and Charting in school (Math Concept) to understand the concept of Percentage.

Upper primary school mathematics question UPQ203

80% of the people in the Esplanade concert hall were adults. 75% of the children in the concert hall were boys. There were 36 more boys than girls. Some boys left the concert hall, after which 10% of the remaining people in the concert hall were boys. How many boys left the Esplanade concert hall?

 Solution:

             Draw the model

 

 

            From the model

                                    The boys were 36 more than girls at first

                                    2 units = 36

                                    1 unit = 18

                                    Total number of people = 20 × 18 = 360

                                    Total number of adults and girls = 17 × 18 = 306

                                    Total number of boys at first = 3 × 18 = 54

                                    The ratio of adults and girls to boys at first = 306 : 54 = 34 : 6 = 17 : 3 = 153 : 27

                                    The ratio of adults and girls to boys at the end = 9 : 1 = 153 : 17

                                    27 units = 54

                                    1 unit = 2

                                    The number of boys left the concert hall in term of units = 27 – 17 = 10

                                    The number of boys left the Esplanade concert hall = 2 × 10 = 20

Alternative solution:

 

 

                        Consider the remaining

                        Boys more than girls by 75% – 25% = 50%

                        36 ==> 50%

                        The number of people remain = 36 × 2 = 72

                        Total people in the hall = 72 ÷ 20% = 360

                        Total number of boys in the hall at first = 72 × 75% = 54

                        Total girls in the hall = 36 ÷ 2 = 18

                        Total adults in the hall = 360 × 80% = 288

                        Finally, Girls plus adults in the hall = 18 + 288 = 306

                        Girls plus adults in the hall is 90%

                        90% ==> 306

                        10% ==> 34

                        Boys finally in the hall = 34

                        The number of boys left the Esplanade concert hall = 54 – 34 = 20

 More Questions on Fraction and Ratio. Click here…

More Questions on Percentage. Click here….

More Questions on Problem Sum. Click here…

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