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