<span>let x = the original no. of students then (x+10) = the actual no. that went on the trip : = the original cost per student and = the actual cost : Original cost - actual cost = $12.50 - = 12.50 multiply equation by x(x+10) x(x+10)* - x(x+10)* = 12.50x(x+10) Cancel the denominators
1500(x+10) - 1500x = 12.5x(x+10) 1500x + 15000 - 1500x = 12.5x^2 + 125x Combine on the right to form a quadratic equation 0 = 12.5x^2 + 125x - 15000 Simplify, divide equation by 12.5 x^2 + 10x - 1200 = 0 You can use the quadratic formula; a=1; b=10; c=-1200, but this will factor to (x + 40(x - 30) = 0 The positive solution is what we want here x = 30 students in the original group Check this by finding the cost per student for each scenario 1500/30 = $50.00; original cost 1500/40 = $37.50; actual cost --------------------- saving: $12.50</span>
