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?

The total number of students that liked dancing after the addition of the new boys is 252

Step-by-step 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

98%

step-by-step explanation: