Question

A group of girls decided to go on a trip and the organizer said that the bus would cost 360$ to rent. The organizer also told them that if they got 3 more girls to go on the trip each girl could pay 6$ less. How many girls ended up going

Answer 1

Let x is number of girls going (x>0).
Since the bus cost 360, each of them paid: $\frac{360}{x}$
If they got 3 more, each would pay: $\frac{360}{x+3}$
According to statement:$\frac{360}{x}$ - 6 = $\frac{360}{x+3}$
⇒(360 - 6x)(x+3) = 360x
⇒360x - 6x^2 +3*360 -18x = 360
⇒6x^2 + 18x - 3*360 = 0
⇒6(x-12)(x+15) = 0
⇒x = 12 (because x > 0)
Thus, 12 girls went.