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

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!

Answer 2

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