At a community food-packing day, the helpers were grouped as adult men, adult women, boys or girls. There were 40% more adult men than adult women and 50% more girls than boys. Altogether, 330 people helped, and the number of males was exactly the same as the number of females.
- Use the equal numbers of males and females to show that the ratio of adult women to boys is 5 : 4.
- Calculate the number of adult women who helped at the food-packing day.
Need a hint?
Write the number of males as adult men + boys and the number of females as adult women + girls. Compare the two differences.
Worked answer
- Equal male and female totals mean that the extra adult men equal the extra girls.
- The extra adult men are 25 of the adult women, while the extra girls are 12 of the boys.
- Thus 25 × adult women = 12 × boys, giving adult women : boys = 5 : 4.
- Use 5 units for adult women and 4 units for boys; adult men are 7 units and girls are 6 units.
- The four groups contain 5 + 7 + 4 + 6 = 22 units altogether.
- 330 ÷ 22 = 15 people per unit.
- Adult women = 5 × 15 = 75.
Answer: 75 people
The mistake this question tests
Habit
Stopped at one part in ratio
Some pupils may compare adult men with boys and adult women with girls directly. The equal totals must instead be written as adult men + boys = adult women + girls.
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