Question

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

75

Explanation:

Answer 2

This is the concept of algebra, to get the total number of dancers we proceed as follows. Let total number of dancers be x;
number of girls will be:
40/100*x
=0.4x
When the number of girls increase by 15, the new number of dances will be:
x+15 dancers
The new number of girls will be:
0.4x+15
since the new number of girls have increased to 52%, then the total number of dancers will be:
(0.4x+15)/(x+15)*100=52
(0.4x+15)/(x+15)=0.52
0.4x+15=0.52(x+15)
solving for x we get
0.4x+15=0.52x+7.8
putting like terms together and simplifying we get:
-0.12x=-7.2
thus
x=-7.2/(-0.12)
x=60
thus the total number of dancers on the floor was 60