Question

This is 22 points

Initially, $40\%$ of the students at the school dance are girls. Then, $15$ more girls arrive, after which $52\%$ of the students at the dance are girls. How many students are now at the dance after the additional girls arrive?

Answer 1

let the initial number of girls be x, this represents 40% of the dancers.
Total number of dancers will therefore be:
100/40*x=2.5x
When 15 more girls joined, the new number of girls was:
x+15 this represents the total percentage of 52%. The new number of dancers became:
2.5x+15:
therefore the new percentage of girls can be expressed as follows:
(new number of girls)/(new number of dancers)×100
(x+15)/(2.5x+15)×100=52
(x+15)/(2.5x+15)=0.52
x+15=0.52(2.5x+15)
x+15=1.3x+7.8
15-7.8=1.3x-x
7.2=0.3x
x=7.2/0.3=24
The number of students after additional number of girls will be:
2.5x+15
=2.5×24+15
=60+15
=75 students

Answer 2

Answer: There are 112 students left.

Step-by-step explanation: let the original number of students be 100 out of which 40 were girls. Additional 15 girls came making a total of 115 students out of which 55 are girls.

But we're told that the number of girls left is 52 not 55 so it means 3 girls left the dance, this reducing the total number of students from 115 to 112.

I believe this is clear enough.

The above solution is correct if the figures 40, 52, and 15 are taken as numbers NoT percentage. That was my error. I'm so sorry!