SOLUTION: A college charters a bus for $1700 to take a group to a museum. When six more students join the trip, the cost per student drops by $7.50. How many students are in the original gro

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A college charters a bus for $1700 to take a group to a museum. When six more students join the trip, the cost per student drops by $7.50. How many students are in the original gro      Log On


   

Question 647079: A college charters a bus for $1700 to take a group to a museum. When six more students join the trip, the cost per student drops by $7.50. How many students are in the original group?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A college charters a bus for $1700 to take a group to a museum.
When six more students join the trip, the cost per student drops by $7.50.
How many students are in the original group?
:
Let n = number to students in the original group
then
1700%2Fn = the original cost
:
(n+6) = no. when six more students join
and
1700%2F%28%28n%2B6%29%29 = the cost when six more join
:
Original cost - six more cost = 7.50
1700%2Fn - 1700%2F%28%28n%2B6%29%29 = 7.50
:
multiply by n(n+6), results:
1700(n+6) - 1700n = 7.5n(n+6)
1700n + 10200 - 1700n = 7.5n^2 + 45n
:
Combine as a quadratic equation
7.5n^2 + 45n - 10200 = 0
:
simplify, divide thru by 7.5
n^2 + 6n - 1360 = 0
:
You can use the quadratic formula, but this will factor to:
(n+40)(n-34) = 0
:
the positive solution
n = 34 original students
:
:
Check this, find the actual cost for each scenario
1700/34 = $50.00
1700/40 = $42.50, a $7.50 difference