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?
\(\phantom{after which 52}\)
+128474 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
