Question

The ratio of children to adults at a party is 2:3. A busload of 30 more children

arrives at the party, and now the ratio of children to adults is 3:2. How many
people were at the party before the bus arrived?

Answer 1

Let's assume the number of children at the party before the bus arrived was "c". Then, the number of adults was "3c/2".

After the bus arrived, the number of children is "c + 30", and the number of adults is still "3c/2".

The new ratio of children to adults is 3:2, so:

c + 30 = (3c/2) * 3/2

Expanding the right side:

c + 30 = (9c/4)

Subtracting "c" from both sides:

30 = (9c/4) - c

Adding "c" back to both sides:

30 + c = (9c/4)

Multiplying both sides by 4:

120 + 4c = 9c

Subtracting "4c" from both sides:

120 = 5c

Dividing both sides by 5:

c = 24

So there were 24 children at the party before the bus arrived, and 3 * 24/2 = 36 adults.

The total number of people at the party before the bus arrived was 36 + 24 = 60

Answer 2

60 people

Explanation:

Before

C:A

2:3

After

C:A

3:2

We know that the number of adults never change.

Before

C:A

4:6

After

C:A

9:6

difference in units of children= 9-4

= 5

5 units= 30

1 unit= 30÷5

= 6

total units [before]= 4+6

= 10

10 units= 6×10

=60