Answer:
252 students at the party like to dance
Step-by-step 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
[tex]\frac{g}{t}=\frac{60}{100}[/tex]
[tex]\frac{g}{t}=\frac{3}{5}[/tex]----------------------------------(1)
We also know that
[tex]\frac{g}{t+20}=\frac{58}{100}[/tex]
[tex]\frac{g}{t+20}=\frac{29}{50}[/tex]-----------------------------(2)
We now have a system of equation from (1) and (2)
3t=5g
[tex]g = \frac{3t}{5}[/tex] ------------------------(3)
50g=29t+580------------------------(4)
Substituting 3 in 4, we get
[tex]50(\frac{3t}{5})=29t+580[/tex]
[tex](\frac{150t}{5})=29t+580[/tex]
[tex]30t =29t+580[/tex]
[tex]30t -29t = 580[/tex]
t =589
So originally there was 580 students
In this 580 students 40% liked to dance
Then the number of students liked to dance =
=> [tex]40\% \text{of} 580[/tex]
=>[tex]\frac{40}{100} \times 580[/tex]
=>[tex]0.4 \times 580[/tex]
=> 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
