Answer:
The number of girls that go to the nursery in the morning are 28 girls
Step-by-step explanation:
The question is a word problem and the parameter given are as follows;
The number of children that go to the nursery, n = 60
The ratio of girls to boys = 3 : 2
The number of periods the children can attend the nursery = 2, morning or afternoon
The proportion of the children that go to the nursery in the morning = 3/4
The proportion of the children that go to the nursery in the afternoon = All those that do not go in the morning
The number of boys that go to the nursery in the afternoon = 7 boys
Let, 'x', represent the number of girls in the school, and let 'y', represent the number of boys in the school
Therefore, we have the following possible equations;
x + y = 60
x:y = 3:2
Therefore, the proportion of the total number of children that go to the nursery that are girls, x = 3/(3 + 2) = 3/5
The number of girls that go to the nursery, x = n × 3/5 = 60 × 3/5 = 36 girls
The number of girls that go to the nursery, x = 36 girls
∴ The number of boys that go to the nursery, y = 60 - 36 = 24 boys
The number of boys that go in the morning = y - (The number of boys that go to the nursery in the afternoon)
∴ The number of boys that go in the morning = 24 boys - 7 boys = 17 boys
The total number of children that go to nursery in the morning = 3/4 × (The number of children that go to the nursery, n)
∴ The total number of children that go to nursery in the morning = 3/4 × 60 = 45 children
The number of girls that go to the nursery in the morning = (The total number of children that go to nursery in the morning) - (The number of boys that go in the morning)
Therefore, the number of girls that go to the nursery in the morning = 45 children (girls + boys) - 17 boys = 28 girls
The number of girls that go to the nursery in the morning = 28 girls
