Answer: The total number of students that liked dancing after the addition of the new boys is 252
Explanation:
Let us denote the total number of students at the party before the addition of the 20 boy students by "a".
Before the addition of of the new boys, 60% of the students at the party were girls. The actual number of girls before the addition =
(60/100) × a
= 3a/5 (number of girls before the addition)
After adding 20 boy students, the total number of students should now be "a + 20"
If the percentage of the girls in the party dropped to 58% from 60%, then the number of girls after the addition of the new boys will now be:-
58/100 × (a+20)
= (58a + 1160)/100 (number of girls after the addition)
Since the number of GIRLS at the party CANNOT increase after the addition of BOYS ONLY, then:
3a/5 = (58a + 1160)/100
Then cross multiplying;
3a × 100 = 5 × (58a + 1160)
300a = 290a + 5800
10a = 5800
a = 580
The total number of students at the party before the addition of the new boys was 580.
Now, if 40% of the total number of students at the party before the addition of the new boy students liked to dance, then the actual number of students that liked to dance is:
40/100 × 580
= 232 students.
If the newly added 20 students also liked to dance, then the current total number of students at the party that liked dancing is:
232 + 20
= 252 students.
After the addition of the 20 new boy students, the total number of students at the party that liked dancing will now be 252