At a science centre on a Saturday, the number of men is 13 of the number of women. The number of boys is 3 times the number of girls. The number of children is the same as the number of adults.
- What fraction of the total number of visitors were women? Give your answer in the simplest form.
- What percentage of the total number of visitors were girls?
Need a hint?
Draw the bar model with men as 1 unit and women as 3 units. Then work out how the children compare with the adults before you find the total.
Worked answer
- (a) Let 1 unit be the number of men. Then women = 3 units.
- Adults = men + women = 1 + 3 = 4 units, so children = 4 units.
- Let 1 part be the number of girls. Boys = 3 parts, so children = 3 + 1 = 4 parts.
- Children are 4 units and 4 parts, so 1 unit = 1 part. Girls = 1 unit, boys = 3 units.
- Total visitors = 1 + 3 + 3 + 1 = 8 units. Women = 3 units, so the fraction is 3/8.
- (b) Girls = 1 out of 8 units, so the fraction is 1/8.
- 1/8 = 12.5/100, so 1/8 of visitors were girls, which is 12.5%.
The mistake this question tests
Stopped at one part in ratio
Pupils often take the men and women ratio as the whole group, or treat 'children equal adults' as a separate count. Each child group must be matched to the same unit size before adding up the total.
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