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

triangle abc is reflected on the line x=-6.5 then reflected again on the x axis

step-by-step explanation:

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step-by-step explanation: