There are 40 boys and 60 girls at the barbecue. The fraction of students that are girls is ½ or 50%. The percent of vegetarian girls among all students is 30%.
Step-by-step explanation:
To solve this problem, we will break it down into steps focusing on each part of the question.
Part A: Number of Girls and Boys
The ratio of boys to girls given is 4:6. To find the actual numbers, we notice that the ratios add up to a total of 10 parts (4+6). Since there are 100 students, each part equals 10 students (100 ÷ 10). Therefore, there are 40 boys (4 parts) and 60 girls (6 parts).
Part B: Fraction of Girls
The fraction of students that are girls at the bar-b-que is the number of girls divided by the total number of students. With 60 girls out of 100 students, the fraction is ⅔ or ½.
Part C: Percent of Vegetarian Girls
Since the ratio of vegetarian girls to omnivorous girls is 1:1, half of the girls are vegetarian. This means that 30 girls are vegetarian since half of 60 is 30. To find the percentage of the total number of students that are vegetarian girls, divide 30 by 100, which gives us 0.30, or 30 percent.