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