Question 209245
let t = number of teens


"they split the $600 total cost equally" ___ 600 / t


" If they had had 5 fewer people, each person would have paid $10 more" ___ 600/(t - 5) = (600/t) + 10


multiplying by t(t-5) ___ 600t = 600t - 3000 + 10t^2 - 50t


subtracting 600t and dividing by 10 ___ 0 = t^2 - 5t - 300


factoring ___ 0 = (t + 15)(t - 20)


t + 15 = 0 ___ t = -15 ___ negative number not realistic


t - 20 = 0 ___ t = 20


substituting ___ $600 / 20 = $30