Question

Of the students attending a school party, 60% of the students are girls, and 40% of the students like to dance. After these students are joined by 20 more boy students, all of whom like to dance, the party is now 58% girls. How many students now at the party like to dance?

Answer 1

252 students at the party like to dance

Explanation:

Given:

60% of the students are girls

40% of the students like to dance

20 more boy students

Percentage of the girls in the party = 58%

To Find:

How many students now at the party like to dance=?

Solution:

Let the number of girls be g.

Let the number of total people originally be t.

We know that

`(g)/(t)=(60)/(100)`

`(g)/(t)=(3)/(5)`----------------------------------(1)

We also know that

`(g)/(t+20)=(58)/(100)`

`(g)/(t+20)=(29)/(50)`-----------------------------(2)

We now have a system of equation from (1) and (2)

3t=5g

`g = (3t)/(5)` ------------------------(3)

50g=29t+580------------------------(4)

Substituting 3 in 4, we get

`50((3t)/(5))=29t+580`

`((150t)/(5))=29t+580`

`30t =29t+580`

`30t -29t = 580`

t =589

So originally there was 580 students

In this 580 students 40% liked to dance

Then the number of students liked to dance =

=>
`40\% \text{of} 580`

=>
`(40)/(100) * 580`

=>
`0.4 * 580`

=> 232

We also know that with these people, 20 boys joined, all of whom like to dance.

Now the number of students like to dance = 232+20 = 252 students