Question

60 children go to a nursery. The ratio of girls to boys is 3 : 2

The children go to the nursery either in the morning or in the afternoon.
Three quarters of the children go to the nursery in the morning.
The rest of the children go to the nursery in the afternoon.
7 boys go to the nursery in the afternoon.
Work out how many girls go to the nursery in the morning.

Answer 1

The number of girls that go to the nursery in the morning are 28 girls

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

Answer 2

Girls (Morning) = 16

Explanation:

60 children go to a nursery. The ratio of girls to boys is 3 : 2

Number of Boys = 3 / (3 + 2) * 60 = 3/5 * 60 =36

Number of Girls = 2 / (3 + 2) * 60 = 2/5 * 60 = 24

Three quarters of the children go to the nursery in the morning.

Number of children (Boys + Girls) = 3/4 * 60 = 45

The rest of the children go to the nursery in the afternoon.

Number of children (Boys + Girls) = 60 - 45 = 15

7 boys go to the nursery in the afternoon.

Boys + Girls = 15

Girls (Afternoon) = 15 - Boys = 15 - 7 = 8

Work out how many girls go to the nursery in the morning.

Girls (Morning) + Girls (Afternoon) = Girls (Total)

Girls (Morning) + 8 = 24

Girls (Morning) = 24 - 8

Girls (Morning) = 16