Sarin’s family attend concert at the Esplanade Part 8 (Math Question)

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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).

Read also postings on Sarin learns concept of ratio in school to understand Ratio.

Upper primary school mathematics question UPQ122

There were 260 people in the Esplanade concert hall last Sunday. There were ¼ time as many children as men and 5/27 times as many children as women in the concert hall. How many more women than men were there in the concert hall? Solution:

                          The ratio of children to men = 1 : 4 = 5 : 20

                          The ratio of children to women = 5 : 27

                          Children : men : women = 5 : 20 : 27

                          Children : men : women : all = 5 : 20 : 27 : 52

                          From the combine ratio,

                          52 units = 260

                          1 unit = 5

                          Different of women to men is 27 – 20 = 7 units

                          There were 5 × 7 = 35 more women than men in the concert hall.

Alternative solution 1:

                      Using math model,

                          Number of units for all people in the concert hall = 5 + 20 + 27 = 52

                          1 unit = 260 ÷ 52 = 5

                          Number of units different men and women = 27 – 20 = 7

                          The number of women more than men = 5 × 7 = 35

Alternative solution 2:

                          Using Equations:      

                          Define C : number of Children, W : number of women M : number of Men

                          Children was ¼ of Men then C = ¼ M or M = 4C

                          Children was 5/27 of women then C = 5/27 W or W = 27/5 C

                          Total people = 260

                          260=C+M+W

                          260=C+4C+27C/5

                          260×5=25C+27C

                          C=25

                          M=4×25=100 (men)

                          W=260-125=135 (women)

                          The number of women more than men =135-100=35

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