SOLUTION: Guidance it needed with this problem please. "Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the dist

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Guidance it needed with this problem please. "Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the dist      Log On


   

Question 69718: Guidance it needed with this problem please.
"Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by %5. How many students attended the get-together?"
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
"Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by %5. How many students attended the get-together?"
:
Let x = Number of actual students that attended
(x+5) = number that planned to attend
:
Original cost per student: 500/(x+5)
Actual cost per student: 500/x
:
500/x = 1.05[500/(x+5)]
:
500/x = 525/(x+5)
:
Cross multiply
525x = 500(x+5)
525x = 500x + 2500
525x - 500x = 2500
25x = 2500
x = 2500/25
x = 100 students attended
:
Check using cost per student:
Actual: 500/100 = $5 per
Planned: 500/105 = $4.76 per
5% Percent increase: 1.05 * 4.76 = $4.998 ~ $5