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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,

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