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?

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Guest Jun 20, 2022

#1**+2 **

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

CPhill Jun 20, 2022