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Initially, 40% of the students at the school dance are freshmen. Then, 15 more freshmen arrive, after which 60% of the students at the dance are freshmen. How many students are now at the dance after the additional freshmen arrive?

 

\(\phantom{after which 52}\)

 Jun 20, 2022
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F = freshmen at first     T = total students at first

 

Initially

 

F / T  = .40   ⇒     F =  .40T      (1)

 

 

After 15 more Freshmen arrive  we have that

 

[F + 15] / [ T + 15 ] =  .60       (2)

 

Sub (1) into (2)

 

[ .40T  + 15 ] / [ T + 15]  =  .60        multiply both sides by  T + 15

 

.40 T + 15  =  .60 [ T + 15 ]

 

.40T  + 15 =  .60T  + 9

 

15 - 9  =  .60T - .40T

 

6   = .20T

 

6 / .20  = T  =   30

 

So....after the 15 arrive.....there are now    30 + 15 =  45  students at the dance

 

 

cool cool cool

 Jun 20, 2022

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