MATH SOLVE

2 months ago

Q:
# This is 22 pointsInitially, $40\%$ 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?

Accepted Solution

A:

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)Γ100

(x+15)/(2.5x+15)Γ100=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

=2.5Γ24+15

=60+15

=75 students

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)Γ100

(x+15)/(2.5x+15)Γ100=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

=2.5Γ24+15

=60+15

=75 students