SOLUTION: A college charters a bus for $1500 to take a group of students to see a Broadway production. When 10 more students join the trip, the cost per student decreases by $12.50. How many

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Question 1019503: A college charters a bus for $1500 to take a group of students to see a Broadway production. When 10 more students join the trip, the cost per student decreases by $12.50. How many students were in the original group?

Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
This deals with cost, prices, and the unknown number of original students. Prices are ratios, and cost is just a money quantity. Try thinking through the description and to formulate equations and expressions.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A college charters a bus for $1500 to take a group of students to see a Broadway production.
When 10 more students join the trip, the cost per student decreases by $12.50.
How many students were in the original group?
:
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